Democratic leadership spoke with President Trump on Sunday in an effort to persuade him to convince Senate Majority Leader Mitch McConnell to hold a vote on their universal background checks bill.

In a statement, House Speaker Nancy Pelosi and Senate Minority Leader Charles E. Schumer said they offered to join him in a “historic signing ceremony” at the White House should it pass the Senate.

“This morning, we made it clear to the President that any proposal that does not include the House-passed universal background checks legislation will not get the job done,” they wrote. “We will not stop until these bills are passed and our children’s lives are safe. We call upon Senator McConnell to ‘Give Us a Vote!’”

According to the White House, the conversation between party leaders was “cordial,” but the president made no commitments regarding the Democrats’ background check bill.

“Instead [he] indicated his interest in working to find a bipartisan legislative solution on appropriate responses to the issue of mass gun violence. The President reiterated his commitment for his administration to continue work on these issues,” Deputy Press Secretary Judson Deere wrote in a statement.

The bill in question, which passed earlier this year on a mostly partisan vote, would extend background checks to private sales — something that gravely concerns conservatives.

Mr. McConnell has not taken up any background check or other gun-control bills since returning from the August recess, saying he is waiting to see what Mr. Trump would be supportive of signing.

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