The government has told Bank of America it needs $33.9 billion in capital to withstand any worsening of the economic downturn, according to an executive at the bank.

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.