The Federal Housing Finance Agency, which oversees the two government-controlled mortgage giants, announced plans to ease credit requirements, simplify documentation and waive certain fees for borrowers seeking to refinance their loans. The program is expected to get off the ground by the summer.

“Last year saw a spike in refinances, but more than 2 million low-income families did not take advantage of the record low mortgage rates by refinancing,” FHFA Director Mark Calabria said.

To benefit from the changes, borrowers would need to make 80% or less of their area’s median income and not have missed more than one mortgage payment in the past 12 months. The program only applies to borrowers with existing loans backed by the mortgage giants and it will be up to lenders to participate in it.

Mr. Calabria said in an interview that the program might help borrowers who suffered a decline in income during the pandemic and who wouldn’t have otherwise qualified for refinancing due to the companies’ underwriting requirements. FHFA estimates that borrowers who take advantage of the new refinance program could save an average of between $100 and $250 a month.

Fannie and Freddie don’t make home loans. Instead, they buy mortgages and package them into securities, which they sell to investors. Their promise to make investors whole in case of default underpins the popular 30-year fixed-rate mortgage.

Despite the pandemic, 2020 brought good news for the mortgage market. The 30-year fixed mortgage rate fell below 3% in July and stayed there for months.

Low rates spurred about 8.8 million homeowners to refinance in 2020, according to Black Knight Inc., a mortgage-technology and data company. Of those, 6.1 million refinanced into loans backed by Fannie and Freddie.

Yet borrowers with less-than-pristine credit—who tend to be lower income—have had trouble refinancing. Mortgage credit availability, a measure of lenders’ willingness to issue mortgages, is near its lowest level since 2014, according to the Mortgage Bankers Association.

The tight lending environment illustrates a growing cleavage in the market: Business is booming for mortgage lenders, but their loans are almost exclusively for borrowers with excellent credit histories, especially for those backed by Fannie and Freddie.

In January 2019, 29.3% of Fannie Mae refinancings were for borrowers with credit scores below 700, according to the Urban Institute. That share dropped to 14.8% in January 2020 and to 9.4% in January 2021. The best rates for loans backed by the companies are generally for borrowers with credit scores above 740.

“Tight credit is a major barrier for many borrowers who want to refinance their mortgages, even though they already have a loan and the rate reduction would make borrowing less risky,” the Urban Institute’s Laurie Goodman and Edward Golding wrote this month.

Democratic lawmakers, consumer advocates and industry officials have pressed FHFA officials in recent months to help lower-income borrowers.

“As rates have fallen, lower income and lower credit score borrowers who may disproportionately benefit from savings on their mortgage seem to be the least likely to receive low-rate refinance loans,” Ohio Sen. Sherrod Brown and a group of Senate Democrats wrote in a November letter to Mr. Calabria.

Among other benefits in the new program, borrowers with loan balances at or below $300,000 wouldn’t have to pay a modest refinancing surcharge imposed by Fannie and Freddie in December. They would also receive an appraisal credit of as much as $500.

Consumer advocates and housing experts welcomed the relief but said it was an open question how many borrowers it would benefit. Some questioned why borrowers would need credit approval for a refinancing, since Fannie and Freddie already own the risk of their loan. Others said that borrowers in a forbearance plan—which allows them to skip monthly payments and make them up later—probably wouldn’t qualify for the new program, though they may still be eligible for a conventional refinancing.

“This is a good start,” said Ms. Goodman. “It seems that the streamline refinance program could have been more expansive and encompass more borrowers.”