Wells Fargo & Co. is rolling out a new mortgage for borrowers making minimal down payments, an offering that could allow the bank to step back significantly from a controversial Federal Housing Administration program.

The move comes as most of the country’s main banks exit from any substantial role making loans guaranteed by the FHA. The agency insures mortgages made to buyers who would otherwise have a hard time getting loans, but it has been shunned by banks following a wave of lawsuits by the Justice Department that alleged poor underwriting.

Wells Fargo, which made $6.3 billion in FHA-backed loans last year, is the only mainstream bank in the FHA’s top 20 originators, according to trade publication Inside Mortgage Finance.

​The bank’s new mortgage allows borrowers​with credit scores​as low as 620 on a scale of 300 to 850​to make down payments of as little as 3%, while also allowing them to use income from family members or renters to qualify. The requirements don’t represent a significant expansion of mortgage access, but will allow Wells Fargo to make more loans to low- and middle-income borrowers without going through the​FHA.

The bank’s new program, which was launched through a partnership with mortgage-finance giant Fannie Mae, could replace about of half the bank’s current FHA volume and increase its market share, a person familiar with the matter said.