The Federal Reserve said 15 of the 19 largest U.S. banks would remain healthy in a severe crisis, demonstrating the scope of the recovery of the nation’s financial system since it nearly collapsed in 2008.

Four banks failed at least one of the criteria in the so-called stress tests: Citigroup, Suntrust Banks, Ally Financial and the insurance giant Metlife, the central bank said. Those companies would have to raise more money to buffer themselves if a crippling downturn hit the economy.

Banks that passed the test included Bank of America, J.P. Morgan Chase, Goldman Sachs and Wells Fargo. Now those firms can raise their dividends or buy back shares, which often has the effect of raising their stock prices.

The scenario used to test the banks included unemployment hitting 13 percent, the stock market dropping by half and housing values falling by 21 percent. The Fed said that in such a situation, the country’s 19 biggest banks would lose $534 billion over nine quarters.

The test was a blow to the four firms that did not pass. Shares of Citigroup, Suntrust and Metlife fell 3 to 4 percent in after-hours trading following the Fed’s announcement.

Ally Financial, the Detroit-based auto and home lender, has been planning an initial public offering that would enable it to return its bailout money to the federal government, but the Fed’s evaluation may complicate those plans.

In a statement, Ally said the Fed’s assumptions were “inconsistent” with the company’s view.

“Ally continues to be committed to supporting the U.S. auto industry and executing plans to repay the U.S. taxpayer,” it said.

The verdict on Citigroup came after chief executive Vikram Pandit was paid $15 million in 2011 for his work in helping rescue the bank from near-collapse. The bank was one of the biggest beneficiaries of the bailout.

“Citi remains among the best capitalized large banks in the world,” the bank said in a statement.

The four companies will have to provide plans to the Fed explaining how they will increase their capital to meet the minimum standards. Other firms may also have to submit plans, though the Fed did not specify which ones or how many.

Banks that passed the test heralded the results as a sign that they can move forward with their plans. Morgan Stanley said it will go ahead with a planned acquisition of the Smith Barney brokerage and with dividend payments. J.P. Morgan Chase said it will declare a dividend of 30 cents per share, up from 25 cents per share. It will also launch a $15 billion stock buyback. The firm’s stock surged 7 percent Tuesday.

The Financial Services Roundtable, which represents the largest financial companies, also sought to portray the stress tests in the best light.

Economic data and a Roundtable report show that “tremendous progress has been made by banks since the crisis, and that the U.S. banking system is on very solid footing,” said the Roundtable’s chief executive, Steve Bartlett.

Some are more cautious about how much leeway the government should be giving the banks.

A day before the results were released, Neil Barofsky, former special inspector general for the Troubled Assets Relief Program, or TARP, said the size of the banks was still a problem.

“We haven’t dealt with the too-big-to-fail problem, and the one way to mitigate that is to have really thick capital barriers,” said Barofsky. “Returning capital at this point doesn’t seem like a particularly good idea.”

The Fed originally planned to release the stress tests on Thursday, but it moved up the release when officials realized some of the information might have been released prematurely, according to a senior Fed official.

This was the third round of tests to which the Fed has subjected the banks. This time, the central bank revealed an unprecedented amount of detail about how individual banks would fare under the test.

The first came during the thick of the crisis in 2009. The second occurred a year ago, when the Fed also allowed most of the country’s large banks to raise dividends and buy back shares.

One concern is that allowing banks to raise dividends and buy back shares means that there will be less capital available to them in the event of a financial crisis.

A senior Fed official emphasized that the model the Fed used was conservative, reflecting severely negative economic conditions. The official emphasized that the Fed does not believe that such an outcome is likely.

The Fed tested whether the banks would be able to sustain a 5 percent Tier 1 common capital ratio — a key measure of a bank’s ability to withstand trouble — under the nightmare scenario. Citigroup fell short, coming in at 4.9 percent. SunTrust was projected to fall to 4.8 percent and Ally to 4.4 percent.

Overall, the Fed official said, the largest financial firms are far stronger than they were just before the financial crisis.