As recently as Wednesday, Mr. Biden’s campaign had said he supported the measure, known as the Hyde Amendment. His decision to change positions illustrates the intense pressure he faces as the presumed front-runner for the Democratic nomination for president.

His turnaround was abrupt, particularly because Mr. Biden has grappled for decades with his views on abortion rights. While he has said he supports Roe v. Wade, the Supreme Court ruling that made abortion legal nationwide, he has opposed members of his own party on a number of abortion measures, ascribing his reluctance to his Roman Catholic faith.

In a speech at a gala hosted by the Democratic National Committee in Atlanta on Thursday night, Mr. Biden credited the change, in part, to recent efforts by Republicans to roll back abortion access in states including Georgia and across the country — especially in the South — calling them “extreme laws.”