WASHINGTON — The government's long-awaited "stress-test" results show the financial system, like the overall economy, is healing but not yet healed.

Ten of the nation's 19 largest banks need a total of about $75 billion in new capital to withstand losses in case the recession gets worse, according to the Federal Reserve's findings, released yesterday.

Some of the largest banks are stable, the tests found. Others need billions more in capital. Government officials have said a stronger banking system is needed for an economic rebound.

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

The five other firms found to need more of a capital cushion are all regional banks — Regions Financial Corp. of Birmingham, Ala.; SunTrust Banks Inc. of Atlanta; KeyCorp of Cleveland; Fifth Third Bancorp of Cincinnati; and PNC Financial Services Group Inc. of Pittsburgh.

The banks will have until June 8 to develop a plan and have it approved by their regulators. If they can't raise the money on their own, the government said it's prepared to dip further into its bailout fund.

The stress tests are a big part of the Obama administration's plan to fortify the financial system. As home prices fell and foreclosures increased, banks took huge hits on mortgages and mortgage-related securities they were holding.

The government hopes the stress tests will restore investors' confidence that not all banks are weak, and that even those that are can be strengthened. The government has said none of the banks will be allowed to fail.

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. Of those losses, $185.5 billion would be from mortgages, $82.4 billion from credit card loans and $53 billion from commercial real estate loans — the loans on banks' books that analysts say are now most vulnerable to default.

Together, the firms that took the test hold two-thirds of the assets and half the loans in the U.S. banking system.

Among the banks that the government did not ask to raise more capital were JPMorgan Chase & Co., brokerage house Goldman Sachs Group Inc., insurer MetLife Inc. and credit card companies Capital One Financial Corp. and American Express Co.

Wells Fargo and Morgan Stanley said they'll try to raise billions in fresh capital. Meanwhile, American Express became the first major financial institution to formally request permission to return federal bailout money provided under the Troubled Asset Relief Program.