NEW YORK (AFP) - Billionaire Donald Trump says he regrets retweeting an unflattering picture of the wife of arch-rival Ted Cruz, in a rare act of contrition from the Republican presidential frontrunner.

Mr Trump is in pole position to seize the Republican nomination but is doing poorly nationwide among female voters, polls show, and faced stern criticism from all sides in recent days after saying women who have illegal abortions should be "punished", before he backtracked.

The billionaire real-estate mogul has been engaged in an increasingly personal war of words with Senator Cruz, his nearest challenger in the Republican race for the White House, that even drew in their wives.

An anti-Trump political group unveiled a controversial campaign ad ahead of votes in Arizona and Utah last month that used a GQ magazine photograph of Mr Trump's wife Melania lying naked and handcuffed to a briefcase.

Sen Cruz denied being behind the ad, which was accompanied by the words: "Meet Melania Trump, your next first lady."

Mr Trump then retweeted a photo compilation of an unflattering photo of Sen Cruz's wife Heidi next to Melania, a Slovenian-American jewelry designer and former model.

"Yeah, it was a mistake," Mr Trump said of the retweet, talking to The New York Times columnist Maureen Dowd, in a column published on Saturday (April 2).

"If I had to do it again, I wouldn't have sent it."