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JPMorgan Chase paid $1 billion to resolve an array of government investigations last week. But its biggest battles with federal authorities may still lie ahead.

The nation’s largest bank is bracing for a lawsuit from federal prosecutors in California who suspect that the bank sold shoddy mortgage securities to investors in the run-up to the financial crisis, according to people briefed on the matter.

The case, expected as soon as Tuesday, could foreshadow other actions stemming from the bank’s crisis-era mortgage business. Federal prosecutors in Philadelphia, the people briefed on the matter said, are also investigating JPMorgan’s sale of mortgage securities.

Underscoring the breadth of the scrutiny, the people said, the Justice Department and the Department of Housing and Urban Development have discussed the possibility of striking a wide-ranging settlement to conclude many of the looming mortgage investigations from federal authorities and state attorneys general. A proposed settlement figure of about $20 billion was discussed at the bank, according to people briefed on the matter, but it is not clear who proposed that number.

The looming legal threats are not isolated to the bank’s mortgage business. After JPMorgan recently resisted a settlement with the nation’s commodities trading regulator, the people briefed on the matter said, the agency began drafting a lawsuit connected to the bank’s multibillion-dollar “London whale” trading loss last year. The agency, which argued that the London trading position was so large that it manipulated the market for financial contracts known as derivatives, sought an approximately $100 million fine and an acknowledgment of wrongdoing from the bank.

JPMorgan initially refused to make such an admission — disputing the accusations and fearing the admission could set a precedent that would threaten some of the bank’s current trading businesses. But late Friday, the bank quietly approached the trading regulator to reopen settlement talks, the people briefed on the matter said.

JPMorgan declined to comment on the talks with the Commodity Futures Trading Commission. Reuters earlier reported the timing of the lawsuit from the California prosecutors.

The wrangling over the mortgage cases and the trading loss investigation illustrate JPMorgan’s legal quandary. If it settles with authorities, the bank must accept steep fines or concede embarrassing admissions. But if it adopts a more hardball approach, the bank can anger government authorities, prompting years of litigation.

Even a conciliatory stance does not always placate the government. Just days after JPMorgan paid $410 million to the nation’s energy regulator to resolve claims the bank devised “manipulative schemes” to transform “money-losing power plants into powerful profit centers,” federal prosecutors in Manhattan opened an investigation into the same activity.

The difficult legal choices being weighed by the bank — should it settle or should it fight — coincide with an unusual wave of scrutiny for JPMorgan, which is now facing investigations from at least seven federal agencies, several state regulators and two foreign nations. The investigations span across the bank. Its mortgage business, debt collection practices and its hiring of the children of well-connected Chinese officials are all under fire in Washington.

And the threats of litigation from the commodities regulator, the Commodity Futures Trading Commission, come on top of $920 million in fines JPMorgan paid last week to four other regulators investigating the London trading loss. (In another settlement announced last week, JPMorgan agreed to pay $80 million to regulators over accusations that it charged credit card customers for identity theft products they never received.)

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The settlements over the trading loss in London — reached with the Securities and Exchange Commission, the Office of the Comptroller of the Currency, the Federal Reserve and the Financial Conduct Authority in London — laid bare a pattern of “deficiencies” in JPMorgan’s oversight.

The “severe breakdowns,” the regulators said, allowed a group of traders in London to amass the risky derivatives bet with little oversight. When the bet spun out of control, the government said, the traders deliberately “inflated the value” of their positions to mask their losses.

No executive was charged in the cases. But the traders, who deny wrongdoing, face both civil and criminal charges. And under the settlement deal with the S.E.C., JPMorgan took the unusual step of acknowledging that it had violated federal securities laws.

“We have accepted responsibility and acknowledged our mistakes from the start, and we have learned from them and worked to fix them,” Jamie Dimon, the bank’s chief executive, said in a statement last week. “Since these losses occurred, we have made numerous changes that have made us a stronger, smarter, better company.”

But JPMorgan is reluctant to make a habit of conceding defeat, people close to the bank say, particularly when it does not believe that any wrongdoing occurred. The onslaught of investigations has fueled some resentment within JPMorgan, where executives and board members are questioning whether the bank has become something of a punching bag for the government.

The bank initially drew a line with the Commodity Futures Trading Commission. That appeared to soften on Friday, when the bank sought to resume settlement talks with the agency.

In the mortgage cases, though, the bank is continuing to fight. That decision stems in part from a belief at JPMorgan, the people close to the bank said, that the government is punishing it for practices that did not occur under its watch.

The bank, for example, faces investigations into the mortgage business it inherited from Washington Mutual, a troubled lender it purchased amid the crisis.

And Eric T. Schneiderman, the New York attorney general, sued JPMorgan last October, accusing Bear Stearns and its lending unit, EMC Mortgage, of defrauding investors who purchased mortgage securities packaged by the companies from 2005 through 2007. JPMorgan, through a deal backstopped by the government, took over Bear Stearns in 2008.

Shortly after Mr. Schneiderman filed the lawsuit, Mr. Dimon called the action “unfair” during a talk at an event in Washington for the Council on Foreign Relations. JPMorgan, the bank chief said, was being penalized for purchasing Bear Stearns in 2008 as “a favor” to the Federal Reserve.

The roughly $20 billion settlement discussed at the bank, but summarily rejected, might have settled both the Washington Mutual investigations and the New York case, the people briefed on the matter said. It is unclear whether it would have put to rest the mortgage investigation by prosecutors in California.

In that case, led by the civil division of the United States attorney’s office for the Eastern District of California, prosecutors found that JPMorgan flouted federal laws with its sale of subprime mortgage securities from 2005 to 2007. The prosecutors, according to JPMorgan’s quarterly regulatory filing in August, had “preliminarily concluded” that the bank “violated certain federal securities laws.”

The bank also disclosed that it faces a “parallel” criminal inquiry from the same United States attorney’s office.