Exhibit 10.1

SUPPORT AGREEMENT

This SUPPORT AGREEMENT (the “Agreement”) is made and entered into as of September 17, 2012, by and between Nabi Biopharmaceuticals, a Delaware corporation (the “Company”), on the one hand, and each of Mangrove Partners Fund, L.P., Mangrove Partners, Mangrove Capital and Nathaniel August (collectively, the “Mangrove Parties”), on the other hand. For purposes of this Agreement, the Mangrove Parties shall also include any and all parties to the Mangrove Parties’ beneficial ownership report on Schedule 13D, as amended, with respect to Company common stock, as now or hereafter filed with the U.S. Securities and Exchange Commission (the “SEC”).

WHEREAS, the Mangrove Parties filed definitive proxy materials with the SEC in order to solicit proxies to vote at a special meeting of Company stockholders, scheduled to be held on September 24, 2012 (including any adjournments or postponements thereof, the “Special Meeting”), in opposition to the proposals made by the Board of Directors of the Company (the “Board”) in connection with a proposed business combination transaction (the “Transaction”) between the Company and Biota Holdings Limited (the “Opposition Proxy Solicitation”);

WHEREAS, on September 17, 2012, the terms of the Transaction were amended to provide additional economic terms to Company stockholders in connection therewith; and

WHEREAS, the parties believe, in light of the amended Transaction, that it is in the best interests of the Company’s stockholders to resolve their respective views regarding the Opposition Proxy Solicitation;

NOW, THEREFORE, in consideration of the premises and mutual agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, hereby agree as follows:

Section 1. Representations and Warranties of the Mangrove Parties. Each of the Mangrove Parties hereby represents, warrants and agrees that each of the Mangrove Parties has full legal right, power and authority and, in the case of individuals, capacity, to execute, deliver and perform this Agreement, and consummate the matters contemplated hereby; the execution and delivery by the Mangrove Parties of this Agreement and the consummation by the Mangrove Parties of the matters contemplated hereby have been duly authorized by all necessary corporate or other actions; and this Agreement constitutes valid, legal and binding obligations of each of the Mangrove Parties, enforceable against each such Mangrove Party in accordance with its terms.

Section 2. Representations and Warranties of the Company. The Company hereby represents, warrants and agrees that the Company has full legal right, power and authority to execute, deliver and perform this Agreement, and consummate the matters contemplated hereby; the execution and delivery by the Company of this Agreement, and the consummation by the

Company of the matters contemplated hereby have been duly authorized by all necessary corporate actions; and this Agreement constitutes valid, legal and binding obligations of the Company, enforceable against the Company in accordance with its terms.

Section 3. Covenants of the Mangrove Parties. Each Mangrove Party, on behalf of himself or itself, as applicable, in reliance on the covenants and agreements of the Company set forth herein, covenants and agrees as follows.

(a) Termination of Opposition Proxy Solicitation. On the terms and conditions set forth herein, the Mangrove Parties’ Opposition Proxy Solicitation is hereby terminated. In addition, from the date hereof through the completion of the Special Meeting, except in support of the Board’s recommendations on each of the proposals as set forth in the Company’s definitive proxy materials dated August 7, 2012, filed by the Company with the SEC in connection with the Transaction, as such materials may be amended or supplemented from time to time (the “Company Proxy Materials”), neither the Mangrove Parties nor any of their Affiliates (as defined below) will, directly or indirectly, (i) solicit authority, proxies or consents for the voting of any voting or other securities of the Company or otherwise become a “participant,” directly or indirectly, in any “solicitation” of “proxies” or consents to vote, or become a “participant” in any “election contest” involving the Company or the Company’s securities (all terms used herein and defined in Regulation 14A under the Securities Exchange Act of 1934, as amended (the “Exchange Act”) having the meanings assigned to them therein), (ii) seek to advise or influence any person with respect to the voting of any securities of the Company, (iii) initiate, propose or otherwise “solicit” Company stockholders for the approval of shareholder proposals or to vote in opposition to the recommendations of the Board with respect to the proposals set forth in the Company Proxy Materials, (iv) otherwise communicate with the Company’s stockholders or others pursuant to Rule 14a-1(l)(2)(iv) under the Exchange Act, (v) otherwise engage in any course of conduct with the purpose of causing stockholders of the Company to vote contrary to, or withhold votes from, the recommendation of the Board on any matter presented to the Company’s stockholders for their vote at the Special Meeting or challenging the policies of the Company, (vi) form, join or in any way participate in any “group” pursuant to Rule 13d-5 under the Exchange Act with respect to any Company securities, other than a “group” that includes all or some lesser number of the members of the Mangrove Parties, but does not include any other members who are not currently Mangrove Parties, (vii) deposit any securities of the Company in a voting trust or subject any securities of the Company to any arrangement or agreement with respect to the voting of the securities of the Company, or (viii) otherwise act, directly or indirectly, alone or in concert with others, to seek to control or influence the management, the Board, policies or affairs of the Company; provided, however, the obligations and restrictions of the Mangrove Parties and their Affiliates set forth in this Section 3(a) shall immediately cease to have any effect or applicability in the event that the Transaction is further amended on economic terms any less favorable than the terms set forth in the amended Transaction.

(b) Vote in Accordance with the Board’s Recommendation. At the Special Meeting, the Mangrove Parties shall, and shall cause their respective Affiliates to, cause all voting securities of the Company beneficially owned by each of them to be present at such meeting for purposes of establishing a quorum and to be voted in accordance with the

2

recommendation of the Board on each of the proposals set forth in the Company Proxy Materials. No later than five (5) business days prior to the Special Meeting, the Mangrove Parties shall, and shall cause each of their respective Affiliates to, vote in accordance with this Section 3(b). The Mangrove Parties shall not, and shall cause each of their respective Affiliates not to, revoke or change any vote in connection with the Special Meeting. The voting obligations of the Mangrove Parties and their Affiliates set forth in this Section 3(b) shall immediately cease to have any effect or applicability in the event that the Transaction is further amended on economic terms any less favorable than the terms set forth in the amended Transaction.

(c) Compliance. The Mangrove Parties shall cause their respective “Affiliates” (as such term is defined in Rule 12b-2 promulgated by the SEC under the Exchange Act) to comply with the terms of this Agreement.

(d) No Other Proposals. Until the completion of the Special Meeting, the Mangrove Parties shall not, and shall cause their Affiliates not to, execute any written consent to approve any proposal by any other stockholder of the Company that has not been recommended by the Board; provided, however, nothing herein shall limit the ability of the Mangrove Parties and their Affiliates to execute any written consent to approve any proposal by any other stockholder of the Company that has not been recommended by the Board in the event that the Transaction is further amended on economic terms any less favorable than the terms set forth in the amended Transaction.

(e) Public Announcement. Promptly but in any event no later than two (2) business days following the public announcement by the Company of the amendment of the terms of the Transaction, the Mangrove Parties shall issue a press release stating that (i) the Mangrove Parties withdraw their opposition to the Transaction and are terminating the Opposition Proxy Solicitation, (ii) the Mangrove Parties unequivocally support the amended Transaction on its current economic terms and (iii) the Mangrove Parties will vote in accordance with the recommendations of the Board on each of the proposals described in the Company Proxy Materials, as long as the Transaction is not further amended on economic terms any less favorable than the terms set forth in the amended Transaction.

Section 4. Covenants of the Company. The Company covenants and agrees, in reliance on the covenants and agreements of the Mangrove Parties set forth herein, to reimburse the Mangrove Parties for their reasonable and documented out-of-pocket fees and expenses incurred (including proxy solicitation, legal and public relations) in connection with the Opposition Proxy Solicitation and related matters and the negotiation and execution of this Agreement and all related activities and matters. In no event shall the costs and expenses to be reimbursed by the Company pursuant to this Section 4 exceed $100,000 in the aggregate. The Company shall reimburse such amounts to the Mangrove Parties by wire transfer, in accordance with instructions provided by a representative of the Mangrove Parties, on the next business day following the completion of the Special Meeting.

Section 5. Mutual Non-Disparagement. Until the earlier of (i) the consummation of the amended Transaction or (ii) any further amendment of the Transaction on economic terms

3

any less favorable than the terms set forth in the amended Transaction, each of the Company and the Mangrove Parties, on behalf of themselves and their officers, directors, partners, managers, members, and agents with actual authority to speak for them with regard to the Opposition Proxy Solicitation or to the Transaction, expressly acknowledges, agrees, and covenants that he, she or it will not make any statements, comments, or communications that are reasonably likely to be considered to be disparaging of or derogatory or detrimental to, the good name or business reputation of, in the case of the Company, the Mangrove Parties, and, in the case of the Mangrove Parties, the Company, or in each case any of their respective members, partners, officers, directors, employees or representatives (including statements relating to the circumstances leading up to and including the execution and delivery of this Agreement). Where applicable, this mutual non-disparagement covenant applies to any public or private statements, comments, or communications in any form, whether oral, written, or electronic. Each of the Company and the Mangrove Parties further agree he, she or it will not knowingly encourage or solicit any such statements, comments, or communications. Nothing in this Section 5 shall limit the ability of (i) any member of the Board from and after the date hereof from taking any action required to carry out his or her fiduciary duty or (ii) the Mangrove Parties from and after the date hereof from making any filings with the SEC reasonably determined to be required according to their legal counsel so long as neither such filing nor the disclosure provided therein is prohibited by the terms of this Agreement.

Section 9. Miscellaneous.

(a) Severability. If any provision of this Agreement shall be held invalid or unenforceable, such invalidity or unenforceability shall attach only to such provision and shall not in any manner render invalid or unenforceable any other provisions of this Agreement.

(b) Consent to Jurisdiction. Each of the parties hereto hereby irrevocably and unconditionally consents to submit to the exclusive jurisdiction of the courts of the State of Delaware and of the United States of America, in each case located in the County of New Castle, for any action, proceeding or investigation in any court or before any governmental authority arising out of or relating to this Agreement and the transactions contemplated hereby (and agrees not to commence any action, proceeding or investigation relating thereto except in such courts), and further agrees that service of any process, summons, notice or document by registered mail to its respective address set forth in this Agreement shall be effective service of process for any action, proceeding or investigation brought against it in any such court. Each of the parties hereto hereby irrevocably and unconditionally waives any objection to the laying of venue of any action, proceeding or investigation arising out of this Agreement or the transactions contemplated hereby in the courts of the State of Delaware or the United States of America, in each case located in the County of New Castle, and hereby further irrevocably and unconditionally waives and agrees not to plead or claim in any such court that any such action, proceeding or investigation brought in any such court has been brought in an inconvenient forum.

(c) Waiver of Jury Trial. Each of the parties hereto hereby irrevocably waives all right to trial by jury in any action, proceeding or counterclaim (whether based on contract, tort or otherwise) arising out of or relating to this Agreement or the actions of the parties hereto in the negotiation, administration, performance and enforcement hereof.

4

(d) Governing Law. This Agreement and the rights and duties of the parties hereto shall be governed by and construed in accordance with the internal laws of the State of Delaware applicable to contracts made and performed therein, without regard to principles of conflicts of law.

(e) Entire Agreement. This Agreement sets forth the entire understanding of the parties in respect of the specific matters contemplated herein and supersedes all prior agreements, arrangements and understandings, written or oral, between the parties hereto relating to the subject matter hereof.

(f) Amendment or Waiver. This Agreement may not be amended, modified or changed, and none of the terms, covenants, representations, warranties or conditions hereof may be waived, except by a written instrument signed by the party against whom enforcement of any change or modification is sought, or in the case of a waiver, by the party waiving compliance. The failure of any party at any time or times to require performance of any provision of this Agreement shall in no manner affect the right at a later time to enforce same.

(g) Notice. Any notice or other communication required or permitted to be given hereunder shall be in writing and shall be effective (i) when personally delivered or delivered by telecopy (with confirmation of transmission) on a business day during normal business hours at the address or number designated below or (ii) on the business day following the date of mailing by overnight courier, fully prepaid, addressed to such address, whichever shall first occur. The addresses for such communications shall be:

5

(h) Headings. The headings herein are for convenience only, do not constitute a part of this Agreement, and shall not be deemed to limit or affect any of the provisions hereof.

(i) Successors and Assigns. This Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective successors and permitted assigns.

(j) Further Assurances. The parties hereto shall execute and deliver such further documents and do such further acts as any party hereto shall reasonably require in order to assure and confirm to the parties hereto the rights hereby created or to facilitate the full performance of the terms of this Agreement.

(k) Counterparts. This Agreement and any amendments hereto may be executed and delivered in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original, but all of which taken together shall constitute one and the same agreement, and shall become effective when counterparts have been signed by each party hereto and delivered to the other parties hereto, it being understood that all parties need not sign the same counterpart. In the event that any signature to this Agreement or any amendment hereto is delivered by facsimile transmission or by e-mail delivery of a “.pdf” format data file, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such facsimile or “.pdf” signature page were an original thereof.

(l) Assignment. Neither this Agreement nor any rights hereunder may be assigned by either party in whole or in part, without the prior written consent of the other party.

(m) Expenses. Except as provided in Section 4 of this Agreement or as otherwise agreed to by the parties in writing, the Company and the Mangrove Parties shall pay all of their own expenses incurred in connection with the implementation of this Agreement. Each party hereto has retained its own counsel and such counsel has advised each party with respect to the subject matter of this Agreement.

6

(n) Remedies. It is hereby agreed and acknowledged that it will be impossible to measure in money the damages that would be suffered if the parties fail to comply with any of the obligations herein imposed on them and that in the event of any such failure, an aggrieved person will be irreparably damaged and will not have an adequate remedy at law. Any such person, therefore, shall be entitled to injunctive relief, including specific performance, to enforce such obligations and to prevent breaches or threatened breaches of this Agreement, without the posting of any bond, and, if any action should be brought in equity to enforce any of the provisions of this Agreement, none of the parties hereto shall raise the defense that there is an adequate remedy at law.

[Signature pages follow]

7

IN WITNESS WHEREOF, the parties hereto have executed and delivered this Agreement or have caused this Agreement to be duly executed and delivered by their respective authorized officers as of the date first set forth above.