COLUMBUS, Ind. — Gov. Mike Pence of Indiana, the Republican vice-presidential nominee, suggested Saturday that he might release his tax returns before Election Day, even as his running mate has shown no inclination of doing the same.

Breaking with campaign custom, the Republican presidential nominee, Donald J. Trump, has refused to release his returns. On Friday, the Democratic presidential nominee, Hillary Clinton, and her running mate, Senator Tim Kaine of Virginia, made public their own 2015 returns, while pointedly noting that Mr. Trump had not.

On Saturday morning, at a campaign stop in his hometown, Columbus, Ind., Mr. Pence ignored questions from reporters about whether he would release his returns. But in an interview with Rita Cosby of WABC Radio that aired on Saturday, he hinted, though he did not promise, that his returns could become public.

“When my forms are filed and when my tax returns are released it’s going to be a quick read, Rita,” Mr. Pence said.