WASHINGTON – The government is changing the terms of its bailout agreement with Fannie Mae and Freddie Mac in a way that will shrink the holdings of the two mortgage giants more quickly and will require payment to the government of all quarterly profits the companies earn.

The Treasury Department announced the changes Friday in an effort to deal with concerns that the companies could at some point exhaust the federal support they were guaranteed when they were taken over by the government in September 2008 during the financial crisis.

The two firms would have to turn over all profits they earn every quarter. They would also be required to accelerate the reduction of their mortgage holdings to hit a cap of $250 billion by 2018, four years earlier than planned.

Under the new arrangement, the firms’ portfolios can be no larger than $650 billion each at the end of this year.

The Obama administration unveiled a plan last year to slowly dissolve Fannie and Freddie, with the goal of shrinking the government’s role in the mortgage system. The proposal would remake decades of federal policy aimed at supporting Americans’ ability to buy homes and could make home loans more expensive.

“With today’s announcement, we are taking the next step toward responsibly winding down Fannie Mae and Freddie Mac while continuing to support the necessary process of repair and recovery of the housing market,” said Michael Stegman, who serves as Treasury Secretary Timothy Geithner’s counselor on housing policy.

Industry groups including the American Bankers Association and the Mortgage Bankers Association were generally supportive of the action.

“Much more work needs to be done to reform the secondary market (for mortgage-backed securities) but today’s announcement helps move this process forward and ensure the taxpayers’ investment is ultimately repaid,” Frank Keating, president of the banking group, said in a statement.

Republicans in Congress, who have often clashed with Democrats over housing policies, were critical, saying the changes don’t answer the more important need to overhaul how the government promotes home ownership.

“Four years after (Fannie and Freddie) were taken over by the federal government, taxpayers are left holding the bag without a plan and without a clue what the future of the secondary mortgage market will look like,” said Senate Republican leader Mitch McConnell of Kentucky. “The Obama administration should stop delaying efforts to work with Congress to end these failed institutions, protect American taxpayers and develop a sustainable long-term plan for reform.”