To the long list of those picking fights with banks over bad mortgages, add the Federal Reserve.

Two years after the Fed bought billions of dollars in mortgage securities as part of the financial bailout, its New York arm is questioning the paperwork — and pressing banks to buy some of the investments back.

The Federal Reserve Bank of New York and several giant investment companies, including Pimco and BlackRock, have singled out Bank of America, which assembled more than $2 trillion of mortgage securities from 2004 to 2008.

Bank of America is already dealing with the fallout from the fight over whether foreclosures were handled properly. It insists that no foreclosures have been initiated in error, and on Monday announced it would resume the foreclosure process in 23 states where court approval is required to go ahead.

But while the human toll of the foreclosure crisis has grabbed the headlines, the fight over how these loans were created in the first place could last longer and ultimately cost the banks much, much more. And it is setting the stage for a huge battle between mortgage holders like the government, hedge funds and other institutional investors on one side and the big banks on the other.

“It’s very serious,” said Glenn Schorr, an analyst with Nomura Securities. “The numbers are all over the map.”

If the Fed and the investors succeed, it could cost Bank of America billions of dollars. On Wall Street and in bank boardrooms, the question of whether investors can force banks to buy back, or “put-back,” the bad mortgages to the banks that sold them is dominating the debate and worrying analysts, money managers and banking executives.

It also makes for some strange bedfellows. After all, it was the government that bailed out Bank of America — twice — during the financial crisis, the same government that includes the Fed.

And it is going to be a fight. On Tuesday, after watching its shares get pummeled again, Bank of America went on the offensive, vowing to “defend the interests of Bank of America shareholders,” and hire more lawyers.

“It’s loan by loan, and we have the resources to deploy in that kind of review,” said Brian T. Moynihan, Bank of America’s chief executive, on a conference call to discuss the bank’s results for the third quarter.

Although the bank turned in better results than expected, much of the call was given over to the put-back issue. “We have thousands of people who are willing to stand and look at these loans,” Mr. Moynihan told analysts. “We’d love never to talk about this again and put it behind us, but the right answer is to fight for it.”

The legal battle turns on the question of whether the banks properly represented the loans they put together into mortgage-backed securities when they sold them to investors. If the banks ignored evidence that the underlying mortgages did not conform to underwriting standards or they lacked the proper paperwork, the banks could be obligated to buy the troubled mortgages back.

The Federal Reserve Bank of New York and the other large investors are pressing Bank of America to buy back a portion of the $47 billion in mortgages it originated, most of which were assembled by Countrywide Financial just before the real estate boom turned to bust in 2005, 2006 and 2007.

Countrywide, which specialized in subprime mortgages, was acquired by Bank of America in July 2008.

“People did not think bondholders would be able to organize themselves, but they can,” said Kathy Patrick, a Houston lawyer who is leading the effort. “It’s a large amount of money but the principle is simple. When you promise to do something in an agreement, you should do it.” A letter from Ms. Patrick detailing the claims was obtained by The New York Times.

The danger posed by angry — or opportunistic — investors ‘putting-back’ mortgages to the banks is hardly limited to Bank of America. Other giants like Citigroup and JPMorgan Chase face similar claims, and last week JPMorgan set aside $1.3 billion just for legal costs, including put-backs.

JPMorgan has said it expects repurchases of mortgages to run at about $1 billion a year, but that expense should be covered by $3 billion it has earmarked specifically for put-backs.

At Bank of America, repurchases have been running at about half a billion dollars a quarter. The bank estimates total put-back claims stand at $12.9 billion, as of Sept. 30. In the third-quarter, Bank of America recorded an $872 million expense for put-backs.

Besides the major institutions, hedge funds like York Capital and Moore Capital have been jumping into the game recently, buying up bad debt in the hopes it will eventually be bought back, according to traders and money managers. Both funds declined to comment.

And smaller ones are sniffing around, hoping to ride the depressed securities higher as the fight over put-backs gathers steam.

“Any hedge fund with a distressed desk is contemplating this trade,” said one analyst who insisted on anonymity. “The idea of bottom-fishing vulture funds buying this stuff up for a nickel on the dollar so they can sue the banks to get 100 cents must be pretty odious for the Treasury, which bailed out the banks in the first place.”

Indeed, the group that includes the Fed is one of two coalitions that is gearing up for a fight with the banks.

Bill Frey, chief executive of Greenwich Financial Services, leads a group of investors that holds just under $600 billion worth of mortgage-backed securities.

But it is the recent controversy over foreclosures that has jump-started interest by pension funds, hedge funds and other players. “In the last two weeks, there has been a flood of new investors,” Mr. Frey said. “We haven’t even had a chance to do the arithmetic, that’s how fast they’re coming in.”

Besides all the lawyers that billions can buy, the banks have other weapons in their arsenal. Some hedge funds and other investors are nervous about challenging the banks too forcefully, because they trade with them daily.

There is risk too for the government, despite the Federal Reserve claims. If the banks are indeed forced to spend tens of billions to buy back securities, they could turn once again to the federal government for help.

Given the legal resources available to the banks, though, that is unlikely to happen quickly. And for now, broader conditions in the financial services are improving. On Wednesday, Bank of America reported that operating earnings in the third quarter hit $3.1 billion, in contrast to a loss a year ago.

A substantial portion of the profit gain came from the expectation of lower losses among credit card and mortgage borrowers, rather than new business, but the bank was able to recapture money it had earlier set aside. It released $1.8 billion from reserves, compared with a release of $1.45 billion in the second quarter.

On a noncash basis for the quarter, the bank reported a loss of $7.3 billion because of a $10.4 billion write-down in the value of its credit card unit, attributed to federal regulations that limit debit fees and other charges.