The Federal Housing Finance Agency said it could reduce the loan limit to $600,000 from $625,500 in the nation’s highest-cost areas, which include cities like Los Angeles, New York and Washington. The limit would drop in much of the rest of the country to $400,000 from $417,000.

The regulator said it would seek public comment before enacting the plan. If adopted, the plan “will not affect loans originated before Oct. 1, 2014,” the agency said.

The housing market imploded during the 2007-09 recession, but has turned a corner in the last year, supported by the Federal Reserve’s low-interest-rate policies and by a taxpayer backstop for most of the mortgage market.

The loan limits were raised in 2008 to help keep the market liquid during the financial crisis, and the Federal Housing Finance Agency had begun to consider lowering them as the housing market recovered as a way to open up more space for private capital.

Fannie Mae and Freddie Mac, which were seized by the government at the height of the financial crisis, do not make loans. They purchase mortgages from lenders, which they either keep on their books or bundle into securities that they offer to investors with a guarantee. They now back about two-thirds of new home loans.