Treasury countered by noting that banks, including JPMorgan Chase, think the department's asking prices are too high. Unable to agree on a price, some institutions are letting the department sell the warrants in public auctions.

While risky for both sides, the auctions give Treasury political cover amid growing criticism that its policies are too easy on big banks.

The shortfall estimated by the Congressional Oversight Panel concerns warrants, financial instruments that allow Treasury to buy shares of the firms at a set price in 10 years. If the stock prices of the banks go up, as they are expected to do, taxpayers could reap a healthy profit.

Treasury obtained the warrants when it began injecting billions into the nation's largest financial institutions in October. They were considered a "deal-sweetener"—a way to help taxpayers benefit from the upside of a financial recovery that depended on billions of federal dollars.

Many large banks received permission to exit the program far earlier than was initially expected. Last month, Treasury announced that 10 of the nation's largest banks—including JPMorgan, Goldman Sachs and Morgan Stanley —could repay about $68 billion of bailout money.

Treasury on Friday said the first large bank has completed negotiations with the government and repurchased its warrants. The government this week received $60 million from State Street of Boston to pay for the stock warrants. State Street had received $2 billion in bailout support from the government and repaid that money on June 17.

Twenty-two smaller banks already have repaid their bailout money, and 11 of those have repurchased their warrants. If the warrants for those firms "had been sold for their true market values, taxpayers would have recovered $10 million more," according to a report Friday from the Congressional Oversight Panel, which was created by Congress to oversee the $700 billion bailout fund.

The warrants were sold at a one-third discount over their true prices, according to the panel's study. If warrants in the more than 600 banks participating in the bailout were sold at such a discount, that would mean taxpayers received $2.7 billion less than the panel estimates the warrants are worth.

Treasury last month announced a method for valuing the warrants through negotiation with the banks. The agency's offers reflect financial modeling and surveys of market participants.

The government also can sell the warrants in auctions instead of negotiating the prices. The panel said Treasury should consider holding open, public auctions to stop "any speculation about whether Treasury has been too tough or too easy on the banks."

Treasury disputed the panel's findings. Department spokesman Andrew Williams said the estimates are based on assumptions, so they may be higher or lower than the actual market prices of the warrants.

"For that reason Treasury is using a more comprehensive approach to valuing the warrants," including obtaining quotes from investors who buy and sell similar securities, he wrote in a statement.

As evidence, Williams pointed JPMorgan's decision to let Treasury sell its warrants at auction—an indication the bank thought Treasury was asking for too much.

"We've taken this action, which is consistent with Treasury's process ... and which allows Treasury to find the true market price," said JPMorgan spokesman Joseph Evangelisti.

Banks have been eager to exit the bailout quickly to avoid the stigma and exempt themselves from restrictions, including limits on executive compensation. Repurchasing the warrants is a necessary step, but has been challenging because of disagreement about the prices.

The oversight panel's analysis was reviewed by three finance professors from Harvard Business School. The panel is headed by Harvard Law School professor Elizabeth Warren. She was the first to propose a new consumer protection agency for financial products, which has become a cornerstone of the Obama administration's reform efforts.

One of the group's Republicans, Texas Rep. Jeb Hensarling, warned against interpreting the report as critical of Treasury's approach to the warrants.

"It is exceedingly difficult to predict the value of financial securities and time the markets over the short term much less the 10-year term of the TARP warrants," he wrote.