The Treasury Department on Wednesday said it will begin another round of sales of the General Motors Co stock it acquired during the government's bailout of the U.S. auto sector.

The Treasury said it will sell an additional 30 million shares of GM common stock in a public offering in conjunction with the company's inclusion to the Standard & Poor's 500 index on June 6. The Treasury intends to sell its shares along with the sale of 20 million shares of GM stock held by the UAW Retiree Medical Benefits Trust, bringing the total size of the sale to 50 million shares.

The move is part of the Treasury's efforts to sell its remaining shares of GM's common stock and wind down the U.S. government's stake in the No. 1 U.S. automaker as part of the financial bailout known as the Troubled Asset Relief Program.

The Treasury, which still owns 241.7 million shares, or nearly 18 percent, of common stock of GM stock, has said it will finish its exit by early next year. In December, Treasury sold 200 million shares of GM stock back to the company.

GM will rejoin the S&P 500 index on Thursday after the close of trading. This is seen as a milestone since the company filed for bankruptcy reorganization in 2009. As a result, GM was kicked out of the S&P 500 slot.

The shares of GM closed at $34.96 on Tuesday, up 1.6 percent.

(Reporting by Margaret Chadbourn; Editing by W Simon and James Dalgleish)