Pedestrians walk by a Bank of America ATM in Charlotte, N.C., near the bank’s corporate headquarters. The bank needs to raise 3.9 billion in capital.

Washington ? The government’s long-awaited “stress-test” results have found that 10 of the nation’s 19 largest banks need a total of about $75 billion in new capital to withstand losses if the recession worsened.

The Federal Reserve’s findings, released Thursday, show the financial system, like the overall economy, is healing but not yet healed.

Some of the largest banks are stable, the tests found. But others need billions more in capital — a signal by regulators that the industry is vulnerable but viable. Government officials have said a stronger banking system is needed for an economic rebound.

Officials hope the tests will restore investors’ confidence that not all banks are weak, and that even those that are can be strengthened. They have said none of the banks will be allowed to fail.

Banks that need more capital will have until June 8 to develop a plan and have it approved by regulators.

Among the 10 banks that need to raise more capital, the tests said Bank of America Corp. needs by far the most: $33.9 billion. Wells Fargo & Co. requires $13.7 billion, GMAC LLC $11.5 billion, Citigroup Inc. $5.5 billion and Morgan Stanley $1.8 billion.

The other five requiring capital are all regional banks: Regions Financial Corp. of Birmingham, Ala., needs to raise $2.5 billion; SunTrust Banks Inc. of Atlanta $2.2 billion; KeyCorp of Cleveland $1.8 billion; Fifth Third Bancorp of Cincinnati $1.1 billion; and PNC Financial Services Group Inc. of Pittsburgh $600 million.

Some of the firms that need more capital already are announcing their strategies. Morgan Stanley, which the government says needs $1.8 billion in new capital, said it plans to raise $5 billion. That will include $2 billion in common stock.

The tests found that if the recession were to worsen, losses at the 19 stress-tested firms during 2009 and 2010 could total $600 billion.

“Looking at the big picture, you can say that things aren’t so bad for the financial industry as a whole,” said Kevin Logan, chief U.S. economist at Dresdner Kleinwort.

But Logan said attracting fresh capital will be a challenge.

“The banking industry is not going to make a lot of money going forward, and that’s a dilemma for keeping banks solvent and getting them lending,” he said.

Financial stocks surged in after-hours trading, after the report was released at 5 p.m. Citigroup shares jumped 8.4 percent to $4.13, while State Street rose 7.3 percent to $40.60. Earlier, the markets had been down.