WASHINGTON (AP)  A top executive of the American International Group has been granted more than a $4 million increase in a pay package because the executive has decided to remain with the company.

The Obama administration’s pay adviser, Kenneth R. Feinberg, approved a request by A.I.G., the insurance giant, to grant the executive a long-term compensation package that included stock options with a current value of $3.26 million and an additional incentive award of up to $1 million. The package comes on top of the person’s 2009 base salary of $450,000.

In a letter released by the Treasury Department on Monday, Mr. Feinberg said he was granting the request so that the executive’s long-term package would be comparable to those already granted to A.I.G.’s other top 25 executives. The executive had been planning to leave the company and had not been granted long-term compensation benefits.

The Treasury, citing privacy restrictions, declined to reveal the executive’s name, and an A.I.G. spokesman said the company would not disclose it, either.