Republican Ted Cruz denounced an article in the National Enquirer tabloid claiming he had extramarital affairs as "garbage, complete and utter lies" and accused his opponent Donald Trump of being the source of the story.

"It's tabloid smear, and it is a smear that has come from Donald Trump and his henchmen," Mr Cruz told reporters at a press conference in Wisconsin, as the battle for the Republican presidential nomination reached new levels of personal rancor.

Mr Trump issued a statement saying he was not responsible for the article.

"I have nothing to do with the National Enquirer and unlike Lyin' Ted Cruz I do not surround myself with political hacks and henchmen and then pretend total innocence," Mr Trump said in the statement.

"Ted Cruz's problem with the National Enquirer is his and his alone, and while they were right about OJ Simpson, John Edwards, and many others, I certainly hope they are not right about Lyin' Ted Cruz."

The National Enquirer could not immediately be reached for comment.

As the pair battle to represent the Republican Party in the 8 November presidential election, Mr Cruz said the story was evidence that Mr Trump is unfit to be president. "This man would be an embarrassment," Mr Cruz said.

The National Enquirer, a tabloid known for its gossip and unflattering celebrity photos, published blurred images of five women with whom it said Mr Cruz has had affairs. The newspaper did not name the women.

Mr Cruz is married to Heidi Cruz, who was campaigning with him today. Mr Cruz gave his wife a hug and kiss before he began the town hall event, and she sat off stage smiling while he spoke.

Two women who appeared to be pictured in the Enquirer stepped forward today and called the article false.

Mr Trump and Mr Cruz have sparred in recent days about their respective wives. Earlier this week Mr Trump accused Mr Cruz of posting a nude photo of Mr Trump's wife, Melania, on Twitter. Mr Trump responded by threatening to "spill the beans" to Mr Cruz's wife.