NEW YORK — The Treasury Department plans to sell its entire 32 percent stake in General Motors within 15 months, eliminating another reminder of the bailouts precipitated by the crash of 2008.

The news came a week after the Obama administration sold its entire stake in American International Group, one of the most controversial rescues during the market crisis.

On Wednesday, the Treasury said it will sell a little less than half of its stake, or 200 million shares, back to GM for $5.5 billion by year’s end. The purchase price of $27.50 is about 8 percent higher than the carmaker’s closing stock price on Tuesday.

The Treasury Department will then sell its remaining 300.1 million shares within the next year to 15 months, depending on market conditions. Those sales could be through stock offerings or other means.

“This announcement is an important step in bringing closure to the successful auto industry rescue,” said Dan Akerson, the carmaker’s chief executive.

The Obama administration stepped in and helped rescue GM and Chrysler in mid-2009 as the two US carmakers struggled. Hoping to forestall a liquidation, Treasury provided financing to the two carmakers and to Ally Financial, GM’s former financing arm.

Ultimately, the administration invested about $49.5 billion in GM, helping guide it through a Chapter 11 filing that shed an enormous amount of debt. It reemerged as a public company in 2010. It has reported rising annual profits for the past two years.

‘‘The government should not be in the business of owning stakes in private companies for an indefinite period of time,’’ said Timothy G. Massad, assistant secretary for financial stability. ‘‘Moving to exit our investment in GM . . . is consistent with our dual goals of winding down TARP as soon as practicable and protecting taxpayer interests.’’