Donald J. Trump’s campaign moved on Sunday to squelch reports — set off by the candidate himself — that Gennifer Flowers, the woman whose claims of an affair with Bill Clinton imperiled his 1992 presidential campaign, would be Mr. Trump’s guest on Monday at his first debate with Hillary Clinton.

In television interviews on Sunday morning, Mr. Trump’s running mate, Gov. Mike Pence of Indiana, flatly denied that Ms. Flowers would attend the debate, at Hofstra University on Long Island. And Mr. Trump’s campaign manager, Kellyanne Conway, said that in threatening on Saturday to invite Ms. Flowers, Mr. Trump had merely been making a point.

“He wants to remind people that he’s a great counterpuncher,” Ms. Conway said on ABC’s “This Week.”

The specter of Ms. Flowers’s attendance arose during a skirmish of psychological warfare between the two campaigns and their supporters in the run-up to Monday night’s matchup.

Mark Cuban, the voluble billionaire who owns the Dallas Mavericks basketball team and is supporting Mrs. Clinton, announced on Twitter on Thursday that Mrs. Clinton’s campaign had given him a front-row seat at the debate to watch her “overwhelm” Mr. Trump.