Two of the world’s biggest banks, facing the threat of criminal charges, are mounting final bids for leniency.

To avoid the fallout from pleading guilty – no giant bank has done so in more than two decades – BNP Paribas and Credit Suisse made last-ditch appeals to prosecutors and regulators in recent weeks, according to people briefed on the talks. The private meetings came after prosecutors sought guilty pleas from the parent companies of both banks: BNP of France over doing business with countries, such as Sudan, that the United States has blacklisted, and Credit Suisse for offering tax shelters to wealthy Americans.

While BNP and Credit Suisse proposed more modest guilty pleas from their subsidiaries rather than parent companies, the people briefed on the talks said, prosecutors appeared to balk at those overtures, challenging broader public concerns that banks have grown so important to the economy that they are effectively “too big to jail.”

In the case of Credit Suisse, which recently created a subsidiary to house the “U.S. offshore business,” prosecutors have privately indicated that they are unwilling to charge the newly formed unit. The bank is now expected to strike a deal with prosecutors as soon as this week, the people briefed on the talks said.

BNP made its own appeals. Underscoring the gravity of a guilty plea for the bank, BNP’s chief executive and two of his top lieutenants traveled to Washington and New York to make their case last week, the people said.

They reserved last Thursday for meeting BNP’s regulators in Manhattan – the Federal Reserve Bank of New York and Benjamin M. Lawsky, New York state’s top financial regulator. At a morning meeting in Lawsky’s conference room overlooking the Statue of Liberty, according to two of the people briefed on the talks, the regulator explained his plans to penalize at least a dozen BNP employees for their role in processing transactions for Sudan and Iran.

But the crucial meeting occurred two days earlier in Washington, the people said, on Tuesday afternoon at the Justice Department’s headquarters. It was there that the executives outlined concerns about a guilty plea to the three prosecutors leading the case: David A. O’Neil, head of the department’s criminal division; Preet Bharara, the U.S. attorney in Manhattan; and Cyrus R. Vance Jr., the Manhattan district attorney.

At the meeting in O’Neil’s second-floor conference room, the BNP executives – Jean-Laurent Bonnafé, the chief executive; Philippe Gijsels, chief strategy officer; and Jean Clamon, head of compliance and internal control coordinator – discussed the potential reverberations of a guilty plea, the people briefed on the talks said. The bank’s lawyers at Sullivan & Cromwell – H. Rodgin Cohen, a dean of the Wall Street legal world, and Karen Patton Seymour, a partner at the firm – accompanied them. Patrick Fitzgerald, a partner at Skadden, Arps, Slate, Meagher & Flom and a former top federal prosecutor in Chicago, also attended the meeting on the bank’s behalf.

The pitch was simple. The executives and lawyers warned that a guilty plea could wreak havoc on BNP and the broader economy well beyond France’s borders.

The argument – playing on the fear that criminal charges could prompt regulators to revoke a bank’s license to operate, the corporate equivalent of the death penalty – helped the British bank HSBC escape criminal charges in 2012. It also stoked a public outcry that Wall Street giants have grown so large and important that they cannot be charged.

But the prosecutors appeared to brush off the concerns, according to the people briefed on the talks, having heard similar appeals in cases involving softer penalties like so-called deferred prosecution agreements. O’Neil and Bharara, in questioning the bank’s lawyers and executives, indicated they had doubts that a guilty plea would imperil the bank or the economy.

The pushback from prosecutors also stemmed from concerns that BNP did not fully cooperate with the investigation. The prosecutors have complained that BNP was too slow to alert authorities to wrongdoing, according to the people briefed on the talks, a delay that might have cost the prosecutors a chance to charge bank employees before a five-year legal deadline.

The investigation, led in part by the FBI in New York, has centered on whether the bank processed transactions for countries that the U.S. government has placed under sanctions. BNP conducted its own internal inquiry that “identified a significant volume of transactions that could be considered impermissible” from 2002 to 2009.

Despite the evidence, prosecutors took a number of precautions when pursuing the guilty plea. In weighing the punishment, the prosecutors held their own meetings with regulators to gain assurances that a guilty plea would not cost the bank its license to operate in the United States.

Without such cooperation, guilty pleas can be elusive. In the case of BNP, prosecutors and regulators cleared the way for a guilty plea at a meeting on April 18. At the meeting, led by the New York Fed’s general counsel, Thomas C. Baxter Jr., regulators signaled that they would not revoke BNP’s charter in the event of a guilty plea. William C. Dudley, the New York Fed’s president, stopped by to lend support to the position that the bank should not escape an appropriate criminal punishment, according to one of the people briefed on the talks.

The BNP and Credit Suisse investigations could lay the groundwork for actions against American banks as well. While the new prosecutorial strategy applies to American banks such as Citigroup, those investigations are at an earlier stage, and it was unclear whether they would warrant criminal charges.