JP Morgan chief executive Jamie Dimon leaves the Justice Department after meeting with Attorney General Eric H. Holder Jr. Dimon and Holder met Thursday morning as the nation’s biggest bank attempts to end federal and state investigations into its liability for selling shoddy mortgage securities. (Gary Cameron/Reuters)

The sage of Wall Street journeyed to Washington on Thursday, but Jamie Dimon’s visit was unlike any the JPMorgan Chase chief has made before.

Dimon sought a meeting with Attorney General Eric H. Holder Jr. in an urgent bid to dispose of multiple government investigations into the bank’s conduct leading up to the financial crisis — and avoid criminal charges. The deal that Dimon discussed with Holder would involve paying the government at least $11 billion, the biggest settlement a single company has ever undertaken, according to several people familiar with the negotiations.

It would also potentially pave the way for other giant banks to reckon with Washington for their roles in the near-collapse of the financial system five years ago. While it would be a historic amount, the fine would still represent a sliver of the damage wrought by the bank for selling mortgage securities that it allegedly knew were worthless.

Dimon, 57, the most prominent of all the Wall Street chieftains, was once mentioned as a possible candidate for Treasury secretary, but in the past year he has faced embarrassing setbacks. In addition to grappling with various government probes, Dimon recently survived a challenge to his leadership after acknowledging a $6.2 billion loss by a JPMorgan trader known as the “London Whale.”

For Holder, 62, meanwhile, a landmark settlement with JPMorgan could help quiet criticism that the Justice Department has failed to hold Wall Street accountable for sparking the housing market’s crash and the ensuing recession. Holder was criticized by lawmakers and consumer advocates this year for saying that some banks had become too big to prosecute.

Holder has taken a direct hand in the negotiations and, in an unusual move, held a 50-minute meeting with Dimon on Thursday. The meeting was “civil,” according to a person familiar with the negotiations, but the talks could still fall apart.

The discussion centered partly on whether the bank could avoid criminal prosecution if it paid the fine and whether it would have to admit guilt. Asked about the negotiations in an unrelated news conference, Holder acknowledged the meeting but snapped at a reporter who suggested that “prison time” was not part of the talks. “You weren’t in the room when I said I was talking to them,” Holder said.

An $11 billion fine would be the largest by far imposed by Justice, far above the $3 billion paid by GlaxoSmithKline in 2011 for illegally pushing antidepressants on consumers. And a person familiar with the matter said the $11 billion represented “a floor” for what JPMorgan would ultimately have to pay to wipe away a host of probes into its mortgage business.

JPMorgan, which declined to comment, is expected to submit another settlement offer soon.

Even at $11 billion or more, the bank would be paying just a fraction of the damage it wreaked on mortgage investors, government agencies and homeowners. And a deal might ensure that no senior executives go to jail, which some experts say would let Wall Street avoid full responsibility.

Finance “is the only field in America where you can commit fraud with impunity and even after you get caught, you can buy your way out of it. And not with your money, mind you, but with shareholders’ money,” said William Black, a former bank regulator who teaches law at the University of Missouri at Kansas City.

Investors have welcomed the negotiations, which intensified this week, sending the firm’s stock up.

“JPMorgan realizes that the market wants it to clean this mess up. And Jamie Dimon, for all of his faults, is one heck of a smart businessman. He wants to end this tsunami of litigation,” said securities lawyer Andrew Stoltmann.

A resolution with Justice would reduce but not end the legal headaches at JPMorgan. There are ongoing federal probes into the bank’s debt-collection practices and its role in the ma­nipu­la­tion of a key interest-rate benchmark, among other matters.

But much of JPMorgan’s legal trouble stems from its mortgage business, which mushroomed through 2008 acquisitions of Bear Stearns and Washington Mutual.

People familiar with the Justice negotiations said a primary factor driving the talks is a lawsuit brought by the Federal Housing Finance Agency over mortgage securities sold by Bear Stearns and Washington Mutual. The securities in contention were bought by mortgage finance companies Fannie Mae and Freddie Mac, which are overseen by the FHFA and cost taxpayers $188 billion to save.

Negotiations, which have been sporadic over the past several weeks, restarted in earnest Monday as federal prosecutors in California prepared to announce civil charges against JPMorgan over the sale of mortgage-backed securities between 2005 and 2007, said the people, who were not authorized to speak publicly.

Facing another lawsuit, JPMorgan returned to the table with an offer of more than $3 billion. But Holder personally rejected the offer, the people said. It is rare for the attorney general to meet with the chief executive of a corporation under investigation, but much is at stake in this case, including Holder’s reputation.

There has been speculation that Holder may step down by the end of the year, and pulling off this record settlement would be a significant accomplishment. Justice has levied multimillion-dollar fines against big banks, including HSBC and Barclays, but to lawmakers and consumer advocates, those penalties are tantamount to a slap on the wrist.

“If I was in [Holder’s] position, I would be concerned about my legacy,” said John C. Coffee Jr., a professor of securities law at Columbia Law School. “There’s been a lot of criticism of officials in Justice being much too soft, timid.”

A sticking point for JPMorgan is whether it will be forced to admit guilt as part of the settlement with Justice, a move that could endanger its defense against similar private litigation.

The bank admitted wrongdoing in a $200 million settlement with the Securities and Exchange Commission last week over its handling of the “London Whale” trading losses. As significant a victory as the admission was for the agency, legal experts said it was a carefully crafted acknowledgment that’s unlikely to harm JPMorgan.

“Justice could craft an admission of wrongdoing that is not an admission of liability,” Coffee said. “You can say we should have been more careful or diligent, but it’s not the same thing as saying we packaged a toxic portfolio and knowingly sold it to suckers.”

Dimon may still be reluctant to confess to misdeeds rooted in the failings of Bear Stearns, a company that JPMorgan bought at the behest of the government.

When New York Attorney General Eric Schneiderman sued JPMorgan in October, alleging the “fraudulent and deceptive” sale of mortgage securities created by Bear Stearns, Dimon vowed to contest the allegations. Now that case may be swept up into the bank’s deal with Justice.

For the venerable JPMorgan, arguably the big bank that emerged strongest from the crisis, to even consider paying $11 billion to the government shows that the bank is beleaguered, analysts say.

“JPMorgan has just north of $20 billion in litigation reserves; $11 billion is a significant hit given the fact it still has . . . a large litany of further liability exposure,” said Joshua Rosner, managing director of the research firm Graham Fisher & Co.

He added: “I don’t know how they can get a deal to work that satisfies JPMorgan’s desire to have a comprehensive settlement and the government’s desire to get a large number.”