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.