has a longstanding bipartisan proposal — written with Senator Patrick J. Toomey, Republican of Pennsylvania — to close legal loopholes that allow people who buy firearms at gun shows or on the internet to avoid background checks.

But the bill has been unable to muster the 60 votes needed to pass the Senate. And Mr. Manchin — who as a moderate from a deeply conservative state is often in the position of deciding whether Democrats can push through their agenda in the evenly divided chamber — also opposes dismantling the legislative filibuster that requires most legislation to win 60 votes.

Mr. Manchin said that he was interested in reviving the Manchin-Toomey legislation, but that he opposed the House-passed universal background check bill, citing its provision requiring checks for sales between private citizens. Separately, Mr. Toomey told reporters that he believed that additional changes would be required to his legislation with Mr. Manchin.

“I want to find something that can pass,” Mr. Toomey told reporters. “That probably would require something that’s a little bit different. We’ve got to see if we can figure out how to thread that needle.”

Glenn Thrush contributed reporting.