The Obama administration is pressing aggressively for a deal to end its support of the American International Group and hopes to have a completed plan to announce by next week, ahead of the midterm elections.

The goal is for the Treasury Department to convert its A.I.G. stake to common stock in a deal that would be completed by the end of the year, according to two people briefed on the negotiations but not authorized to discuss them publicly. The Treasury would sell those shares to private investors over time.

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