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After hinting at it for a day, Donald J. Trump on Wednesday bluntly accused Senator Ted Cruz of “stealing” victory in the Iowa caucuses and demanded a do-over.

Based on the fraud committed by Senator Ted Cruz during the Iowa Caucus, either a new election should take place or Cruz results nullified. — Donald J. Trump (@realDonaldTrump) February 3, 2016

Prior to that, he tweeted:

Ted Cruz didn't win Iowa, he stole it. That is why all of the polls were so wrong and why he got far more votes than anticipated. Bad! — Donald J. Trump (@realDonaldTrump) February 3, 2016

More recently:

The State of Iowa should disqualify Ted Cruz from the most recent election on the basis that he cheated- a total fraud! — Donald J. Trump (@realDonaldTrump) February 3, 2016

Mr. Trump finished in second in Iowa, after leading public opinion polls there for months. Initially, after losing the state, Mr. Trump was gracious, thanking Iowans in his concession speech and offering Mr. Cruz a kind word on his victory. On Tuesday, though, Mr. Trump vacillated between thanking Iowans and saying he was honored by his showing to saying it wasn’t worth spending his own money on the race because voters didn’t appreciate it.

In typical fashion, Mr. Trump first tested lines about Mr. Cruz committing voter fraud in a speech at a rally in New Hampshire, sprinkling it in with a larger address.

Mr. Trump is basing his claim on reports that Mr. Cruz’s aides and allies, including Representative Steve King of Iowa, had posted a false report on Twitter that Ben Carson had suspended his campaign while the voting was still going on. The implication is that some of the Carson votes ended up going to Mr. Cruz.

The Five Stages of Donald Trump’s Grief Over His Loss in Iowa The billionaire businessman initially struck a magnanimous tone after losing the Iowa caucuses on Monday night. It didn’t last long.

Mr. Cruz was brutal in his response to Mr. Trump.

Asked about Mr. Trump’s remarks at a news conference in Goffstown, N.H., on Wednesday, Mr. Cruz assailed Mr. Trump as never before, taunting him as someone who “finds it very hard to lose” and saying a man with his temperament belonged nowhere near “the button.”

“We’re liable to wake up one morning and Donald, if he were president, would have nuked Denmark,” Mr. Cruz said. “That’s not the temperament of a leader to keep this country safe.”

He did not stop there.

“We need a commander in chief, not a twitterer in chief,” one dig began.

He’s losing it,” went another.

“My girls are five and seven,” Mr. Cruz said at one point. “And I’ve got to tell you, Caroline and Catherine are better behaved than a presidential candidate who responds by insulting everyone every day.”

Mr. Cruz also said he did not know anyone “who would be comfortable with someone who behaves this way having his finger on the button” and questioned whether Mr. Trump might skip this week’s New Hampshire debate, as well.

But Mr. Cruz was perhaps most forceful describing Mr. Trump’s history of left-leaning positions, accusing Mr. Trump of supporting “amnesty” for undocumented immigrants, noting the developer’s support for eminent domain and saying his opponent supported “Bernie Sanders-style socialized medicine.”

He repeated his invitation to debate Mr. Trump one-on-one.

“What Donald does, when he loses, is he blames everybody else,” Mr. Cruz said, wrapping up. “It’s never Donald’s fault.”

A spokesman for the Republican Party of Iowa did not immediately respond to an email seeking comment.

In an interview with Boston Herald Radio, Mr. Trump said he “probably” will sue over the results and made clear he believes this is why polls predicting his victory didn’t come true.

“It’s a total voter fraud when you think of it and he picked up a lot of those votes and that’s why the polls were so wrong, because of that,” Mr. Trump said. “I couldn’t understand why the polls were wrong.”

He also cited other irregularities in Iowa, slamming the Cruz campaign for putting out a misleading mailer that appeared to be from the government. It was labeled “VOTER VIOLATION” and warned residents that the secretary of state graded them according to their registration and voter history and they would receive “Fs” if they did not vote.

The Iowa secretary of state has said the mailers misrepresented the role of his office and Iowa election law. It was not clear whether there would be any repercussions.

Katharine Q. Seelye contributed reporting.

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