The Federal Housing Finance Administration (FHFA), overseer of the government-controlled mortgage giants Fannie Mae and Freddie Mac, detailed a plan on Tuesday for the companies’ uncertain futures, grappling with the challenges of political hostility, reluctant private investors and a fragile housing market.

The FHFA said dissolving the companies wasn’t realistic, considering the size of their holdings and their crucial role in housing. Fannie and Freddie buy and guarantee mortgage loans that have been originated by outside lenders, allowing the lenders to offer more mortgages to homeowners.

Ginnie Mae, a government entity under the Department of Housing and Urban Development, has also ramped up its market share. The private sector remains wary of such deals in the uncertain economic climate, and government-backed loans represent virtually all mortgage activity.

Moving forward, the Obama administration, FHFA and industry groups agree that returning private investment to the mortgage market is crucial for limiting the exposure of the government — and by extension, taxpayers — to losses. But encouraging such a move remains elusive, and the government may always have to play some role.

“A central issue remains: whether a government guarantee is essential to a functioning mortgage market,” the FHFA noted.

The FHFA proposed a mortgage securities market that would connect investors directly to homeowners, but one tasked with sidestepping the pitfalls of the last boom by providing more transparency. But before moving to an entirely private system, infrastructure would have to be established to combine Fannie and Freddie’s books, an effort that would require further taxpayer investment — far from guaranteed in the current political environment.

The two entities have already cost taxpayers more than $180 billion since a government takeover in 2008, as the housing collapse submerged their balance sheets. Some politicians have even blamed the entities for causing the housing crisis by increasing their share of subprime mortgages, although it was private investors that had the bulk of such toxic loans.

Congress recently passed legislation limiting the companies’ executive pay, which comes at a time when the CEOs of both Fannie and Freddie have announced that they intend to quit when replacements are found. The FHFA has argued that reducing executive pay hurts its ability to attract top talent and may expose the companies to more losses.

Industry figures welcomed the FHFA’s proposals to increase private involvement in the mortgage market, but questioned the FHFA’s ability to enact such changes.

“I think it’s the right idea,” said Jonathan Miller, president and CEO of real estate appraisal firm Miller Samuel Inc.

“But there’s nothing in their past actions that gives me confidence,” he added, pointing to the record of the FHFA’s predecessor, the Office of Federal Housing Enterprise Oversight, during the housing bubble.

Fannie and Freddie have taken some steps to encourage outside investors. They have raised fees, which may open them to more competition, and are exploring ways of holding part of the mortgage guarantee, while having private investors hold a stake.

Miller commended the move, which could keep lenders involved in the loans they sell.

“That was the problem before. There was no skin in the game,” he said. “The mentality of the banks was to offload the risk.”

However, any drastic changes in policy are unlikely before the presidential election. The FHFA acknowledged that it was up to lawmakers to make the ultimate decision.

“The final chapter, though, remains the province of lawmakers,” said the FHA in its report. “Fannie Mae and Freddie Mac were chartered by Congress and by law, only Congress can abolish or modify those charters.”