While the American International Group comes under fire from Congress over executive bonuses, it is quietly fighting the federal government for the return of $306 million in tax payments, some related to deals that were conducted through offshore tax havens.

A.I.G. sued the government last month in a bid to force it to return the payments, which stemmed in large part from its use of aggressive tax deals, some involving entities controlled by the company’s financial products unit in the Cayman Islands, Ireland, the Dutch Antilles and other offshore havens.

A.I.G. is effectively suing its majority owner, the government, which has an 80 percent stake and has poured nearly $200 billion into the insurer in a bid to avert its collapse and avoid troubling the global financial markets. The company is in effect asking for even more money, in the form of tax refunds. The suit also suggests that A.I.G. is spending taxpayer money to pursue its case, something it is legally entitled to do. Its initial claim was denied by the Internal Revenue Service last year.

The lawsuit, filed on Feb. 27 in Federal District Court in Manhattan, details, among other things, certain tax-related dealings of the financial products unit, the once high-flying division that has been singled out for its role in A.I.G.’s financial crisis last fall. Other deals involved A.I.G. offshore entities whose function centers on executive compensation and include C. V. Starr & Company, a closely held concern controlled by Maurice R. Greenberg, A.I.G.’s former chairman, and the Starr International Company, a privately held enterprise incorporated in Panama, and commonly known as SICO.