WASHINGTON — The U.S. Treasury Department on Thursday set a price of $34.41 per share for the sale of 30 million shares of General Motors stock.

Treasury said the sale will result in aggregate proceeds to the government of $1.03 billion. A United Autoworkers retiree health care trust fund was selling 20 million of its GM shares as well, bringing total sales to 50 million shares.

Treasury set the price for its stock after the markets closed on Thursday. GM stock closed Thursday at $34.44 per share. The stock had closed at $35.49 on Tuesday, the highest closing since December 2010. Shares of GM stock are up about 19 percent since the beginning of the year.

The public offering will help accelerate the government's exit from GM stock, which it got in exchange for a $49.5 billion government bailout of the company in 2008 and 2009.

Late last year the government still owned 500 million shares of the automaker. But in December, GM bought 200 million shares for $5.5 billion. And this year Treasury has been steadily selling its remaining shares of GM stock. Treasury has said it has a goal of completing those sales by early 2014.

GM has been encouraging the government to exit from its partial ownership of the company, hoping to shed the derisive "Government Motors" nickname.

On Thursday GM replaced H.J. Heinz Co. in the S&P 100 and 500 indices. The ketchup maker's acquisition by 3G Capital and Warren Buffett's Berkshire Hathaway is expected to be completed by then. Stocks often get at least a temporary boost after joining the S&P 500 because funds that follow the index have to add the shares to their portfolios.

Treasury said that with the conclusion of this week's stock sale, taxpayers will have recovered $32.53 billion of the $49.5 billion bailout amount, leaving it about $16.97 billion below recovering the entire amount of the bailout. That would mean Treasury will have to sell the remaining 189.2 million shares of GM stock that it still owns for approximately $89.69 to recoup all of the bailout costs.