If the bank is unable to raise the capital cushion by selling assets or stock, it would have to rely on the government, which has provided $45 billion in capital through the Troubled Asset Relief Program.

It could satisfy regulators’ demands simply by converting non-voting preferred shares it gave the government in return for the capital, into common stock.

But that would make the government one of the bank’s largest shareholders.

Executives at the bank, one of the largest being examined, sparred with the government over the amount, which is higher than executives believed the bank needed.

But J. Steele Alphin, the bank’s chief administrative officer, said Bank of America would have plenty of options to raise the capital on its own before it would have to convert any of the taxpayer money into common stock.

“We’re not happy about it because it’s still a big number,” Mr. Alphin said. “We think it should be a bit less at the end of the day.”

The government’s determination that Bank of America doesn’t need as much capital as it has already received from taxpayers is an indication that even some of the most troubled banks may not need more government money than has been allocated to them.

The Treasury Department declined to comment on Tuesday evening.

Citigroup, by contrast, has already decided to allow the government to convert some of its investment into common stock.

Under the arrangement worked out between the Treasury and Citigroup earlier this year, the Treasury will receive mandatory convertible preferred shares, meaning preferred shares that can be converted to voting shares of common stock at the will of the government.

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