WASHINGTON — Goldman Sachs and Morgan Stanley agreed to offer a $557 million package of cash and other assistance for mortgage borrowers to settle a federal inquiry into accusations that the banks improperly seized homes.

The sum includes $232 million in direct payments to more than 220,000 borrowers and $325 million in assistance such as loan modifications, the Federal Reserve said in a statement. Eric Kollig, a Fed spokesman, declined to say how much each of the New York-based firms will pay.