Senator Ted Cruz on Friday accused Donald J. Trump “and his henchmen” of peddling an article in a supermarket tabloid alleging that Mr. Cruz had engaged in extramarital affairs.

Mr. Cruz called the report, published by The National Enquirer, a piece of “garbage,” replete with “utter lies.” He said that “the truth does not matter” to Mr. Trump.

“He will lie and go to sleaze,” Mr. Cruz told reporters after a campaign stop in Wisconsin. “Well, that sleaze has no place in politics, and I hope the American people are fed up with it.”

In a statement, Mr. Trump denied playing any role in The Enquirer’s article.

“I have no idea whether or not the cover story about Ted Cruz in this week’s issue of The National Enquirer is true or not, but I had absolutely nothing to do with it, did not know about it, and have not, as yet, read it,” he said.