CEDAR RAPIDS, Iowa — Joe Biden and Elizabeth Warren, two of the leading candidates for the 2020 Democratic nomination, made the case on Monday for muscular new gun control proposals, but differed on whether it was possible to reach compromise with congressional Republicans.

Mr. Biden said it was not. Ms. Warren seemed more open to the idea.

As much of the Democratic field fanned out across Iowa and New Hampshire to campaign this holiday weekend, Mr. Biden told reporters in Cedar Rapids, Iowa, that the only solution for major new gun control legislation was to defeat Republicans in the elections 14 months away — “flat-out beat them,” as he put it.

Mr. Biden, the former vice president, has made bipartisanship a theme of his campaign and has talked about working with Republicans, including Senator Mitch McConnell. But Mr. Biden took an unequivocal stand on expanded background checks and other measures when asked if there was room to reach a compromise with Mr. McConnell, the Senate majority leader, on legislation following the nation’s latest spate of mass shootings that left 53 dead in August.

“None, none on this. I think this is no compromise. This is one we have to just push and push and push and push and push,” he said. “The fact of the matter is, I think this is going to end with some of them defeated.”