NEW YORK—The Federal Reserve this week issued new guidelines to large bank holdings companies, which will undergo a new round of stress tests to determine whether they are sound enough to restore paying dividends to shareholders.

The move comes after several large U.S. banks have pressured the Fed to allow them to pay dividends.

“The criteria provide a common, conservative approach to ensure that [bank holding companies] hold adequate capital to maintain ready access to funding, continue operations, and continue to serve as credit intermediaries, even under adverse conditions,” a statement from the Fed action said.

The tests will be conducted on the nation’s biggest banks, and will test a bank’s ability to meet Basel III accords standards, taking into consideration severe deterioration of the financial markets and impact of the recent Frank-Dodd Wall Street Reform and Consumer Protection Act.

Most large banks ceased paying dividends in late 2008 when the financial crisis hit the industry. If banks pass the newest stress tests, which will begin in early 2011, the company may start to repay or increase dividends, or undergo other capital changes such as repurchase of stock.

But new stress tests are not a panacea for an industry that was forced to undergo deep changes following the recent financial crisis.

“There is no direct way to calculate how much equity is needed to assure markets that a banking organization is viable,” said Fed Gov. Daniel Tarullo in a speech in Washington last week.

But the new regulatory proposals unveiled in September by the Basel Committee on Banking Supervision agreed upon by 27 nations—the Basel III—will enact the more stringent limits yet on banking firms.

“While there continues to be a relatively high degree of uncertainty about near- to medium-term economic prospects, the basic questions surrounding capital and regulatory reform have now been answered,” Tarullo said. “We anticipate that some firms with high capital levels that have been retaining solid earnings for several quarters will be interested in increasing or resuming dividends.”

This week, regional U.S. bank Comerica Inc. doubled its dividend to shareholders, from 5 cents a share to 10 cents. The dividend increase will be paid on Jan. 1, 2011, to shareholders of record as of Dec. 15.

Bloomberg reported this week that large banks such as Wells Fargo & Co., PNC Corp., and JPMorgan Chase & Co. are eyeing dividend increases in the near future.

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