WASHINGTON—The leader of Senate Democrats moved to take the threat of a government shutdown off the table, following a grueling intraparty fight in which lawmakers struggled with how best to resist President Trump’s fast-paced efforts to slim down federal agencies.

Schumer’s comments are a change in tune from Wednesday when he said that Democrats would not provide the votes needed to approve the House-passed stopgap funding measure. He argued that the Senate should instead vote on a “clean” bill that would maintain spending levels for 30 days to enable bipartisan negotiations.