WASHINGTON – Government stress tests are expected to show that nearly a dozen of the nation’s largest banks do not have enough money to survive if the economy worsens and will need to raise billions of dollars as a precaution.

Findings of the government’s long-awaited tests of 19 banks leaked out Wednesday, a day ahead of an official announcement.

Investors cheered reports that American Express, JPMorgan Chase and Bank of New York Mellon have enough capital to endure and even pushed up the stocks of banks that might need more capital.

But the public nature of the assessments also raised questions among some critics about whether the findings will reflect the banks’ actual conditions.

The tests put banks through two scenarios: one that reflected expectations about the current recession and another that envisioned a recession deeper than what analysts predict.

Citigroup Inc. will need to raise about $5 billion, according to a government official briefed on the results who spoke on the condition of anonymity because he was not authorized to discuss the matter. Earlier news reports had put that dollar figure closer to $10 billion.

Regions Financial Corp. also will need to raise more money, according to people briefed on the results, as will Bank of America Corp. and Wells Fargo & Co.

Bank of America stock rose Wednesday after reports that the Charlotte, N.C.-based company would need to collect $34 billion in additional capital. The New York Times and Wall Street Journal reported the figure. The Journal cited unidentified people familiar with the situation, while the Times quoted a bank executive.

Stress tests have long been a part of the bank regulation system. They help regulators decide how to supervise banks and help banks decide how to limit their risk. Those conversations between banks and regulators normally take place behind closed doors. In recent weeks, the government’s unprecedented decision to publicly release bank-test results has fanned speculation, with analysts predicting the findings and investors staking out trading positions.

Critics are concerned that all the attention could make the tests much less effective. They say regulators seem so intent on maintaining public confidence in the banks that the results will have to say the banks are basically healthy.