Chief executives of the nation's biggest financial institutions emerged from a meeting with U.S. President Barack Obama Friday pledging to cooperate with the White House's effort to steer the economy out of its mess.

Executives said the tone of the more-than-90-minute session was open and cordial, with both sides looking to move beyond recent divisive rhetoric.

"We're just in this together. There's still some hard work to do, but [it was] a pleasant meeting," said Bank of America Corp. (BAC) CEO Ken Lewis.

White House spokesman Robert Gibbs called the get-together a "good, productive and frank conversation."

One participant said the meeting was free of drama. Obama acknowledged that the past few weeks have been rough for banks, but made clear that the general public is angry over excessive compensation. He asked the industry to help rein in the issue.

The CEOs agreed they had to make clear that they understood the public's concern over taxpayer-funded bailouts, according Freddie Mac (FRE) CEO John Koskinen. The executives, however, said government programs need firm rules that don't change with the political winds.

"Whatever the rules are going to be, we need to know them sooner rather than later because we are prepared to play by the new requirements but we need to know what they're going to be," he said.

The bankers said they support the proposal unveiled this week by Treasury Secretary Timothy Geithner to cleanse their balance sheets of toxic assets, though they are waiting for more specifics of the plan.

"We don't know all the details...but we think it's a really encouraging first step to get the plan out there," said Robert Kelly, CEO of Bank of New York Mellon Corp. (BK). "We need to hear the details. I think there's going to be a lot of interest in it."

Richard Davis, CEO of U.S. Bancorp (USB), said a proposal to tax bonuses paid to employees of companies that accept government aid wasn't discussed at the meeting, despite widespread public outrage - and administration rhetoric - over the bonuses doled out to executives at American International Group Inc. (AIG).

"We understand there have been some optics that have been very negative. We apologize for that because it's not something that this industry supports or wants," Davis said.

Gibbs said the session touched on the toxic-asset plan, executive-compensation issues, and a revamp of the U.S. regulatory system. He said Obama was "very pleased" with the meeting and hopes to keep the lines of communications open with Wall Street.

"He had no agenda beyond working to get a solution, the right solution for our financial system, and to get it stabilized and working again for the American people," Gibbs said.

Yet the furor over AIG's bonuses has sparked concerns that banks, worried about government interference in their compensation schemes, may stop participating in the Troubled Asset Relief Program, or TARP, and other government programs. The White House is eager to keep financial institutions involved, but is sensitive to anti-Wall Street sentiment.

The president appealed to the bankers' patriotism, urging them to help the country by boosting lending and helping people get into more affordable mortgages, the executives said. There was little talk of the details of the federal rescue funds received by the industry and whether some banks would seek to return the funds early, they said.

Asked whether the large financial-services companies owed the public an apology for their role in creating the financial mess, Lewis said, "I think there are very few financial institutions who would not say we've made mistakes and that we feel awful bad about the mistakes we have made."

However, he argued it was time to stop dwelling on the errors and work to fix the economy: "At some point you have to stop focusing on the past, and focus on the present." Lewis disputed that he favored reinstating a law that separated commercial-banking operations from that of investment-banking work. He had made remarks coming into the meeting to a reporter that he said were misconstrued. "I think a bank that brings all things to bear is the right way to go," he said.

The thrust of the president's message to the bank executives, Koskinen said, was that the government and the financial industry needed to work together to steer the economy to recovery.

"No one in that room gave any indication at all that they were anything other than enthusiastic about supporting the president and this program," Koskinen said.

Bank of America's Lewis, when asked if his company planned to return government funds it received under TARP, said it was premature to make that decision because banks are still undergoing government-administered stress tests.

JPMorgan Chase & Co. (JPM) CEO Jamie Dimon told CNBC that his bank doesn't have a timetable for returning funds it took under TARP.

One participant said Obama conceded that paying the government back could be a positive event, but said it shouldn't get in the way of lending. The president neither encouraged nor discouraged returning government funds, the person said.

The meeting included JP Morgan's Jamie Dimon, Bank of America's Lewis, American Express Corp. (AXP) CEO Ken Chenault, Freddie Mac's Koskinen, State Street Corp. (STT) CEO Ronald Logue, BONY-Mellon's Kelly, Northern Trust Corp. (NTRS) CEO Rick Waddell, PNC Financial Services Group Inc. (PNC) CEO James Rohr, Goldman Sachs Group Inc. (GS) CEO Lloyd Blankfein, Morgan Stanley (MS) CEO John Mack, Citigroup Inc. (C) CEO Vikram Pandit, Wells Fargo & Co. (WFC) CEO John Stumpf, and U.S. Bancorp's Davis.

Cam Fine of the Independent Community Bankers, Michael Paese of the Securities Industry and Financial Markets Association, and Edward Yingling of the American Bankers Association also attended the session.

-By Henry J. Pulizzi and Jessica Holzer, Dow Jones Newswires; 202-862-9256; henry.pulizzi@dowjones.com