Exhibit 99.1

FOR IMMEDIATE RELEASE

THORNBURG MORTGAGE ANNOUNCES AMENDMENT AND EXTENSION

OF EXCHANGE OFFER AND CONSENT SOLICITATION

SANTA FE, N.M., SEPTEMBER 15, 2008 – Thornburg Mortgage, Inc. (NYSE: TMA), announces that it is amending its Exchange Offer and Consent Solicitation (the “Exchange Offer”) for all outstanding shares of its 8.00% Series C Cumulative Redeemable Preferred Stock (“Series C Preferred Stock”), Series D Adjusting Rate Cumulative Redeemable Preferred Stock (“Series D Preferred Stock”), 7.50% Series E Cumulative Convertible Redeemable Preferred Stock (“Series E Preferred Stock”) and 10% Series F Cumulative Convertible Redeemable Preferred Stock (“Series F Preferred Stock” and collectively with the Series C Preferred Stock, Series D Preferred Stock and Series E Preferred Stock, the “Preferred Stock”) to remove the guaranteed delivery procedures and extend the expiration date.

Holders who wish to tender their shares of Preferred Stock must deliver, or cause to be delivered, their shares and other required documents to the exchange agent before the expiration date. Applicable rules and regulations of the Securities and Exchange Commission (the “SEC”) require us to keep the Exchange Offer open for additional time so that shareholders may review the amendment and, if they desire, withdraw their previously tendered shares. In order to provide holders of the Preferred Stock with the additional time required, the Exchange Offer is extended to expire at 12:01 a.m., EDT, on September 23, 2008, unless further extended or terminated by the company.

Despite this extension, for reasons described below, Thornburg Mortgage believes that it may not be able to close the Exchange Offer unless the company reaches a satisfactory agreement with the reverse repurchase agreement counterparties that are party to the Override Agreement dated as of March 17, 2008, as amended (the “Override Agreement”), who are asserting positions that

are contrary to the company’s understanding with respect to the rights and obligations of the company and the counterparties, respectively, under various agreements. Unless a satisfactory agreement is reached with the counterparties, the conditions that the exchange offer complies with applicable law cannot be satisfied at the present time because Maryland law prohibits the company from paying the cash portion of the consideration offered in the Exchange Offer if, after making the payment, the company would not be able to pay its debts as they become due in the usual course of business or the company’s total assets would be less than the sum of its total liabilities.

Since the commencement of the Exchange Offer, the Override Agreement counterparties have made a series of unanticipated margin calls and have withheld funds payable to the company, and if these actions remain unresolved the company’s available liquidity will be greatly diminished from the level anticipated when the company commenced the Exchange Offer. These actions and the positions asserted by the counterparties are in direct conflict with the Company’s understanding of certain key features of the Override Agreement, including, among other things, whether the aggregate amount of all margin calls under the Override Agreement is subject to a $350 million cap, whether margin calls on downgraded collateral may also be based on changes in the market price for underlying collateral as opposed to changes in haircut only, whether the liquidity fund established by the company as required by the Override Agreement can be used for corporate purposes (other than paying margin calls), whether certain monthly interest collected on collateral and certain proceeds of sales of collateral must be remitted to the company in a timely manner and whether certain counterparties have valid rights of set-off under other agreements with the company. Despite its diligent negotiations to date, Thornburg Mortgage has not been able to reach a satisfactory agreement with the Override Agreement counterparties. Further, the Override Agreement counterparties continue to withhold virtually all cash owed to the company under both the Override Agreement and its warehouse lines. The company continues to attempt to resolve these issues in order to consummate the Exchange Offer, but at this time there can be no assurance that the conditions to closing the Exchange Offer will be satisfied prior to its expiration.

Because of the cash constraints that have been imposed on the company by the Override Agreement counterparties, both in respect of their actions to date and in respect of the prospect of additional margin calls and withholdings of cash in the future, Thornburg Mortgage has initiated the solicitation of a consent from the holders of its Senior Subordinated Secured Notes due 2015 (the “Senior Subordinated Secured Notes”) to agree to accept the interest payment due on their notes on September 30, 2008 in the form of additional Senior Subordinated Secured Notes in principal amount equal to the cash interest payable. All Senior Subordinated Secured Notes will continue to bear interest at a rate of 18% per annum until the Triggering Events, as defined in the indenture governing the Senior Subordinated Secured Notes, are satisfied. Absent improvement in the company’s current liquidity position, holders of at least 98% of the $1.15 billion aggregate principal amount of Senior Subordinated Secured Notes currently outstanding are being requested to agree to the company’s request to forego the receipt of cash interest in order for the company to be able to make the interest payment due on September 30, 2008 and avoid a default. MatlinPatterson Global Investment Advisors and its affiliates, which together hold more than 40% of the outstanding aggregate principal amount of these notes, have stated that they currently intend to agree to the company’s request. The successful completion of this consent solicitation of the holders of Senior Subordinated Secured Notes will not, by itself, enable Thornburg Mortgage to satisfy the conditions to closing the Exchange Offer.

The Exchange Offer is being made to holders of Preferred Stock in reliance upon the exemption from the registration requirements of the Securities Act of 1933, as amended, afforded by Section 3(a)(9) thereof. Investor inquiries about the Exchange Offer should be directed to the company at 866-222-2093 (toll free). Holders of the Preferred Stock are urged to read the Offering Circular dated July 23, 2008 (the “Offering Circular”) and all supplements thereto, which have been filed with the SEC and contains important information regarding the

Exchange Offer. Requests for copies of the Offering Circular, all supplements thereto and related documents may be directed to Georgeson Inc., the information agent for the Exchange Offer, at 866-399-8748 (toll free). The Offering Circular, all supplements thereto and other information regarding the Exchange Offer may also be obtained through the SEC’s Web site at www.sec.gov and the company’s Web site at www.thornburgmortgagetender.com.

This press release does not constitute an offer to purchase or a solicitation of acceptance of the offer, which may be made only pursuant to the terms of the Offering Circular and the related materials.

Thornburg Mortgage is a leading single-family residential mortgage lender focused principally on prime and super-prime borrowers seeking jumbo and super-jumbo adjustable-rate mortgages.

This press release may contain forward-looking statements within the meaning of the federal securities laws. These forward-looking statements are based on current expectations, estimates and projections, and are not guarantees of future performance, events or results. Actual results and developments could differ materially from those expressed in or contemplated by the forward-looking statements due to a number of factors, including but not limited to: the impact of the March 31, 2008 financing transaction; the company’s ability to meet the ongoing conditions of the Override Agreement and ongoing negotiations with the parties thereto with respect to the application of such agreement and the interpretation of certain ambiguities under such agreement; general economic conditions; the company’s ability to meet its interest payment obligations under the Senior Subordinated Secured Notes and whether or not the consent described above will be obtained; ongoing volatility in the mortgage and mortgage-backed securities industry; the company’s ability to complete the Exchange Offer for all of its outstanding Preferred Stock; the company’s ability to raise additional capital; the company’s ability to retain or sell additional assets; market prices for mortgage securities, changes in interest rates and other risk factors discussed in the company’s SEC reports, including its most recent quarterly report on Form 10-Q, annual report on Form 10-K/A, its Proxy Statement for its Annual Meeting held on June 12, 2008, its Proxy Statement for the Exchange Offer Solicitation and its Registration Statement on Form S-3. These forward-looking statements speak only as of the date on which they are made and, except as required by law, the company does not intend to update such statements to reflect events or circumstances arising after such date.

Thornburg Mortgage, Inc., Santa Fe

Investor Relations

505-989-1900

Media contact

Suzanne O’Leary Lopez

505-467-5166

ir@thornburgmortgage.com

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