WASHINGTON — General Motors, not the government, will determine when the automaker will conduct a public stock offering at the heart of the company's revival, the Obama administration said Thursday.

The Treasury Department said in a statement it expects to sell some of its 61 percent stake in GM when the automaker goes public. The initial public offering could happen as early as October.

Treasury provided guidance on how it intends to be involved in GM's much-anticipated stock sale, which is expected to be among the largest initial public offerings in U.S. history. The stock offering is a key part of GM's recovery as it emerges from a government-led bankruptcy last year.

"GM must determine that it is, in all relevant respects, ready to become a public company. For those reasons, it is critical that the process of preparing for a potential IPO be managed by GM," the department said.

Treasury said GM will choose the banks that underwrite the deal, "subject to Treasury's agreement that the selection is reasonable," but the department will determine the fees to be paid to the banks. Major Wall Street banks are trying to become the lead underwriter of the stock sale, but the government is expected to push for low fees related to the stock sale.

In a statement, GM said, "We will launch an IPO when the conditions are right and GM is ready."

The department said the IPO is expected to include the sale of shares by Treasury, GM and other shareholders. The size of the offering and the amounts of primary and secondary shares will be determined later.

The Obama administration has long stressed it is not involved in GM's daily business decisions. But administration officials have said they need to protect taxpayers and recoup as much as possible of the $50 billion in federal aid provided to GM.

GM has said it might sell shares later this year or early 2011. But CEO Ed Whitacre and company officials have said the timing will be determined by the state of the financial markets, the overall health of the auto industry and GM's ability to make progress.

GM has repaid $6.7 billion that the government considered loans.