Fannie Mae headquarters stands in Washington, D.C. (Andrew Harrer/BLOOMBERG)

A federal housing regulator on Tuesday released a plan for beginning to scale back mortgage giants Fannie Mae and Freddie Mac — just as the Obama administration is pressing the taxpayer-backed companies to do more to help homeowners.

The Federal Housing Finance Agency, which oversees Fannie and Freddie, laid out steps to wind down the companies, largely by increasing fees charged to borrowers who take out mortgages. The FHFA’s hope is that as the cost of receiving a taxpayer-backed mortgage goes up, more borrowers will turn to private lenders, whose loans do not carry government backing.

But the effort could conflict with measures being pursued by Fannie and Freddie — and the Obama administration — to increase the government’s role in housing.

A year ago, the administration released a white paper calling for a gradual wind-down of Fannie and Freddie, whose bad bets on risky home loans before the financial crisis have cost taxpayers more than $130 billion.

But for much of the past year, the White House has been going in the opposite direction. Administration officials have been urging Fannie and Freddie to take steps to help homeowners in an effort to lift home values, free up cash in the economy and help borrowers avoid foreclosure.

Officials have been encouraging the companies to reduce debts owed by homeowners, for instance, and to make it easier for borrowers to refinance at lower interest rates. Those measures require Fannie and Freddie to take new risks with taxpayer money, and make the housing market more reliant on the government.

The FHFA, which controls the firms in a legal arrangement known as conservatorship, has resisted taking steps that would burden Fannie and Freddie with more taxpayer losses.

“This is clearly one of the challenges that FHFA faces as conservator,” said Edward DeMarco, acting FHFA director. “We’re getting a clear message about wind-down. At the same time, there are continuing to be calls for . . . Fannie and Freddie to do more.”

The companies are essential cogs in the $10 trillion housing finance market. Operating through the banking system, they connect investors around the world with Americans looking to buy homes.

By pledging that taxpayers will make investors whole if borrowers default, Fannie and Freddie are essentially able to guarantee a plentiful supply of funding for mortgages, making it easier for buyers to get affordable home loans.

Fannie and Freddie, together with the Federal Housing Administration, have dominated the housing market in the past four years as banks withdrew sharply from lending during the financial crisis and recession.

The private market has not bounced back with the rest of the economy. Policymakers are concerned about the risk to taxpayers presented by the government’s large footprint in the mortgage market. The Obama administration plans to publish more details about overhauling housing finance in the coming months.

“The housing sector will continue to be a drag on our economic recovery until we end the ongoing bailout of Fannie and Freddie and replace the existing government-backed mortgage finance system with a purely private market solution,” said Rep. Scott Garrett (R-N.J.), chairman of the congressional subcommittee that overseees the firms.

However, that is not a universal view. Top administration advisers — and many outside economists — say the government must still play a significant role in housing.

“Part of the conundrum for policymakers is we can have some broad consensus on wanting to wind down Fannie and Freddie,” DeMarco said, “but it becomes pretty unclear about what’s left in the marketplace” after they’re gone.

The FHFA’s plan discusses efforts to lay the groundwork for a new mortgage system including, among other things, a new process for pooling loans into bundles and selling them to investors.

The plan also discusses the things that Fannie and Freddie can continue to do to help lessen the nation’s foreclosure crisis without increasing taxpayer losses.

Those include facilitating short sales and deeds-in-lieu, in which a homeowner is forgiven for part of the debt owed to a bank either when selling the home or transferring ownership to the lender.