The U.S. Treasury and Federal Reserve, capping a weekend of high-stakes maneuvering, attempted to shore up confidence in Fannie Mae and Freddie Mac by announcing a plan that placed the federal government firmly behind the battered mortgage giants.

In a statement timed to precede the opening of Asian markets Monday, as well as a closely watched auction of debt by Freddie, the Treasury said it plans to seek approval from Congress for a temporary increase in a longstanding Treasury line of credit for the two companies.

The...