WASHINGTON – The Federal Reserve Board on Tuesday adopted tougher requirements for banks — part of an international agreement designed to prevent another financial crisis — and opened the door to even stricter rules for the nation’s biggest institutions.

The new standards, part of the Basel III accord, require banks to hold more and higher-quality capital to offset potential losses. The rules also change the way the risks of certain types of assets are calculated.

“With these revisions to our capital rules, banking organizations will be better able to withstand periods of financial stress, thus contributing to the overall health of the U.S. economy,” said Fed Chairman Ben Bernanke.

The Fed’s Board of Governors approved the new rules unanimously.

The rules also must be approved by the Federal Deposit Insurance Corp. and the Office of Comptroller of the Currency, which are expected to do so next week.

The new requirements would be phased in starting next year for large banks and in 2015 for small banks.

The vast majority of banks — 95 percent of those with less than $10 billion in assets and all of those with more than that — would have to meet a key new minimum-capital requirement, the Fed said. That requirement is to hold at least 4.5 percent of assets in high-quality capital, up from 2 percent.

About 100 banks would have to raise a total of $4.5 billion by the time the phase-in period ends in 2019 in order to meet another new requirement that allows them to return capital to their shareholders through dividend payments and stock buybacks.

That requirement is to hold an additional 2.5 percent of assets in high-quality capital, bringing the total needed to 7 percent.

Other capital requirements also were increased.

“While strong capital requirements alone cannot ensure the safety and soundness of our financial systems, they are central to good financial regulation, precisely because they are available to absorb all kinds of losses, no matter how unanticipated,” said Federal Reserve Gov. Daniel K. Tarullo.

“Adoption of these rules assures that, as memories of the crisis fade, efforts to build and maintain higher capital levels will not be allowed to wane,” he said.