Even the new rules allow companies some leeway. While giving shareholders a say in bonuses above the cap and restricting when stock incentives can be cashed in, the rules do not place limits on the size of such awards, which have become the biggest part of many compensation packages. In addition, the toughest new rules apply only to large companies seeking government assistance to survive.

They do not apply to the more than 350 institutions that have already received bailout funds, only to those that seek aid under the next phase of the bailout program. And companies that seek aid but do not need exceptional government assistance can waive the $500,000 pay cap, as long as they submit their executive pay policies to a nonbinding shareholder vote.

Still, the rules represent the most comprehensive effort to curb compensation. “This is America,” Mr. Obama said on Wednesday. “We don’t disparage wealth. We don’t begrudge anybody for achieving success. And we believe that success should be rewarded. But what gets people upset — and rightfully so — are executives being rewarded for failure. Especially when those rewards are subsidized by U.S. taxpayers.”

In 2007, the latest year that figures are available, the largest participants in the bailout program paid their chief executives an average compensation of $11 million, including salary, bonus and benefits. Of that amount, according to a review by Equilar, an executive compensation firm, only about $844,000 was cash salary. About $2.5 million was in a cash bonus, with the bulk — $7.4 million — in stock awards, and the remainder in benefits and perks.

If banks return to the government for more money, the new rules would require a reduction in pay, but not in stock awards, though these would be subject to a non-binding vote of the shareholders and would be in the form of long-term incentives because of restrictions on when they could be cashed in.