Banks and rival lenders are butting heads over the credit scores used to decide millions of mortgage requests by U.S. home buyers.

Now, a federal agency is weighing whether to step into the fight, which revolves around a longtime requirement for lenders who sell mortgages to Fannie Mae and Freddie Mac to gauge most borrowers using FICO scores. The Federal Housing Finance Agency's ultimate decision could have wide-reaching ramifications for the mortgage market and home buyers across the U.S.

Mat Ishbia, CEO of a major nonbank lender, United Wholesale Mortgage, said he was enthusiastic about a possible change. "Doing something just because you've always done it that way isn't a good enough reason," Mr. Ishbia said.

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