Republican lawmakers on Friday were urging their colleagues to support a proposal to allow the biggest U.S. banks to get back about $25 billion they have paid to the Federal Reserve.

Reps. Bill Huizenga (R., Mich.) and Steve Stivers (R., Ohio) were circulating a letter to House leaders Friday encouraging them to include the language in a government spending bill Congress will take up next week. About 30 Republicans have signed on to the letter, according to a spokesman for Mr. Stivers.

House...