Sen. Ted Cruz on Friday forcefully denounced a tabloid story floating rumors of extramarital affairs, calling it “complete and utter lies” and saying GOP rival Donald Trump and his team are behind it.

“This garbage does not belong in politics,” Mr. Cruz said of a report in the National Enquirer that said he’d been “caught cheating — with 5 secret mistresses.”

The Texas senator has been in a nasty back-and-forth with Mr. Trump after an anti-Trump political action committee released an ad showing a racy photo of Mr. Trump’s wife Melania from her days as a model. Mr. Trump accused Mr. Cruz of being behind that ad and warned this week that he’d retaliate against Mr. Cruz’s wife, Heidi.

Mr. Cruz, for his part, criticized the racy ad but warned Mr. Trump not to go after his own wife. And on Friday he seemed to put the Enquirer story on Mr. Trump.

“Donald, when he’s losing, when he’s scared, when Republicans are uniting against him, decides to peddle sleaze and slime,” Mr. Cruz said.

“Donald has demonstrated he’s willing to attack anyone and everyone and truth does not matter to him — he will lie and go to sleaze,” he said. “Well, that sleaze has no place in politics, and I think the American people are fed up with it.”

Asked if he would continue to support Mr. Trump if the businessman ultimately is the GOP nominee, Mr. Cruz said: “I will say this: I don’t make a habit out of supporting people who attack my wife and attack my family.”

Mr. Trump said in a statement released by his campaign that he has no idea whether the story is true or not, but that he had absolutely nothing to do with it, did not know about it, “and have not, as yet, read it.”

“Likewise, I have nothing to do with the National Enquirer and unlike Lyin’ Ted Cruz I do not surround myself with political hacks and henchman and then pretend total innocence,” Mr. Trump said. “Ted Cruz’s problem with the National Enquirer is his and his alone, and while they were right about O.J. Simpson, John Edwards, and many others, I certainly hope they are not right about Lyin’ Ted Cruz.”

“I look forward to spending the week in Wisconsin, winning the Republican nomination and ultimately the Presidency in order to Make America Great Again,” he said.

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