WASHINGTON—The Trump administration said it would support returning mortgage-finance giants Fannie Mae and Freddie Mac to private hands, a development that could keep the companies at the center of the housing market for decades to come.

The principles announced Thursday represent a major reversal from what leaders of both parties over the past decade promised—to abolish the companies, which guarantee roughly half the U.S. mortgage market. The approach, which doesn’t require approval by Congress, would mark an important win for investors who have been betting politicians wouldn’t follow through on those promises.

Treasury officials said they would aim to privatize the government-controlled firms without making it tougher and more expensive for people to get mortgages. They generally avoided making specific policy recommendations on how to accomplish these goals in a report released Thursday.

They said they would work with federal regulators to flesh out the details on how to put Fannie and Freddie on a sounder financial footing as well as to curtail the firms’ roles in housing finance. The process could take years to implement and won’t affect existing mortgages.

“Our view is that the government footprint has become too big,” Treasury Secretary Steven Mnuchin said in an interview ahead of Thursday’s report. “There are people in Washington who are happy to leave this the way it is for another 10 or 20 years, and that’s not us. We feel an obligation to try to fix this.”