Sen. Ted Cruz accused Donald Trump and his associates of hawking a false story that the married Texas senator had sexual relationships with five unidentified women.

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OSHKOSH, Wis. — Sen. Ted Cruz on Friday vehemently denied a story in The National Enquirer that accused him of extramarital affairs and blamed rival Donald Trump for planting “complete and utter lies” in the tabloid.

Cruz accused Trump and his associates of hawking a false story that the married Texas senator had sexual relationships with five unidentified women. The claims come amid a nasty feud between the two candidates over their wives that has dominated the Republican presidential race this week.

“Let me be clear, this National Enquirer story is garbage,” Cruz said after a rally at an Oshkosh parking-cone factory, bringing up the subject himself. “It is complete and utter lies. It is a tabloid smear, and it is a smear that has come from Donald Trump and his henchmen.”

Cruz singled out the only named source in the tabloid’s story, former Trump political adviser and longtime GOP operative Roger Stone, who was quoted as saying, “where there is smoke there is fire.” Cruz said Stone was so well-known for his political dirty tricks that he was identified with a vulgar term describing “copulating with a rodent.”

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“Donald may be a rat but I have no desire to copulate with him,” Cruz said. “This garbage does not belong in politics.”

Trump, in a statement, said he had “no idea” whether the story was true and said he had nothing to do with it. “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,” Trump wrote.

Cruz, in turn, labeled the front-runner for the Republican nomination “Sleazy Donald.”

The National Enquirer did not name the women supposedly involved but published photos of five women with their faces blurred out. The Washington Post has not confirmed any of the claims made by the Enquirer.

The saga comes amid the foul and strikingly personal atmosphere of the 2016 Republican presidential race, which has seen attacks leveled on spouses, jokes about the size of genitalia and rivals labeled “con artist,” “sleazy” and “liar.”

One woman who spoke out about the story was Trump’s national spokeswoman, Katrina Pierson, who once worked for Cruz. She said the story was categorically untrue.

“Speaking for myself, the article is trash and 100% false,” Pierson wrote in an email to The Post. She tweeted earlier Friday: “Of course The National Enquirer story is 100% FALSE!!! I only speak to myself, however. Carry on …”

On CNN earlier Friday, a Trump supporter, Boston Herald columnist Adriana Cohen, accused former Cruz staffer Amanda Carpenter during a live television interview of being one of the women cited in the Enquirer story.

Carpenter vigorously denied the accusations. “What’s out there is tabloid trash. If someone wants to comment on it, they can talk to my lawyer. It is categorically false. You should be ashamed for spreading this kind of smut,” she said. “I will not be intimidated. I will continue to make my thoughts known about Donald Trump, and I’m not backing down.”

Cruz, who has been married to his wife, Heidi, for 15 years, pinned The National Enquirer story on Stone, the longtime political adviser to Trump and former aide to Richard Nixon. Trump said he cut ties with Stone in August. Cruz said Stone has “50 years of dirty tricks behind him” and is the only person quoted on the record in the story.

“It is attacking my family. And what is striking is Donald’s henchman, Roger Stone, had for months been foreshadowing that this attack was coming,” Cruz said.

Cruz also pointed to ties between Trump and the Enquirer, which endorsed him this month. New York Magazine has reported that Trump and David Pecker, chief executive of the company that publishes the tabloid, are longtime friends.

In an interview with The Post, Stone accused Cruz of dirty tricks, bringing up accusations that just before Iowa’s caucuses, the senator’s campaign misled the state’s voters about whether then-candidate Ben Carson would remain in the race.

Trump said the Enquirer story didn’t come from him.

The latest chapter in the saga comes after days during which Cruz and Trump engaged in a spat surrounding their wives, one that raised concern amid Republicans that Trump would drive away female voters if he was the nominee for president.

An anti-Trump super PAC not affiliated with Cruz or his campaign circulated ads featuring a risqué, 15-year-old photo of Trump’s wife, Melania, taken for British GQ magazine.

“Meet Melania Trump. Your next first lady. Or, you could support Ted Cruz on Tuesday,” the ad read. It was meant to target socially conservative voters in Utah, whose caucuses Cruz won Tuesday.

On Tuesday, Trump threatened Cruz on Twitter: “Be careful, Lyin’ Ted, or I will spill the beans on your wife!”

Trump did not elaborate on what he had in mind concerning Heidi Cruz, who has recently spoken about a difficult period in her life and marriage in 2005, when she suffered from what Ted Cruz described as “a period of depression.”

Trump later retweeted an unflattering photo of Heidi Cruz alongside a professional one of Melania, a retired model. A visibly angry Cruz blasted Trump as a “sniveling coward” and told him to “leave Heidi the hell alone.”

Cruz was asked Friday whether the tone of the presidential campaign had become childish.

“One person has been childish, and that’s been Donald Trump,” he said. “And one question Americans are wondering all over this country is how low will Donald go? Is there any level to which he is unwilling to stoop?”