GOFFSTOWN, N.H. — Donald Trump, who often­ resorts to stinging Twitter attacks when his presidential campaign appears to be flagging, unleashed a barrage at Ted Cruz Wednesday accusing the Texas senator of fraudulently stealing this week’s Iowa caucus.

It was unclear if Trump had filed formal complaints with the Iowa State Republican Committee to back up his allegation, but the unpredictable businessman once again demonstrated an ability to dominate the news — even when he was not in the state.

“Ted Cruz didn’t win Iowa, he illegally stole it,’’ Trump tweeted, before deleting it and sending it again by removing the word “illegally.’’ “That is why all of the polls were so wrong and why he got more votes than anticipated. Bad!’’

Cruz answered by saying Trump is “losing it’’ and called his outburst a “Trumpertantrum.’’

“I don’t know anyone who would be comfortable with someone who acts this way having his finger on the button,’’ he said. “We’re liable to wake up one morning and Donald — if he were president — would have nuked Denmark.’’

The exchange — much of it focused on activities on a close caucus night two days earlier — highlighted how attacks and counterattacks are accelerating in the days before next Tuesday’s primary vote in New Hampshire. Trump fired off his tweet as he was preparing to fly to Arkansas for a rally.

Cruz, speaking to reporters here after holding the third of four town hall meetings, contrasted his willingness to take question after question with Trump’s decision to jet in and out of the state.

“It seems his reaction to everything is throw a fit, to engage in insults,’’ he said. “And I understand that Donald finds it very hard to lose. . . . But at the end of the day, the Iowa people spoke. Donald Trump guaranteed a victory in Iowa — and then he lost. And he doesn’t like that, and his reaction is that he breaks down.’’

Cruz publicly apologized this week after his campaign and allies stoked rumors before the Iowa caucus that retired neurosurgeon Ben Carson was dropping out of the race. Some Iowa Republicans suggested the rumors amounted to dirty tricks, but not fraud.

Trump’s claims of fraud centered on several late-breaking developments just before Iowans went to caucus sites on Monday night, after reports emerged that Carson was planning to fly home to Florida. While the Carson campaign made it clear he was staying in the race — he was merely heading home to grab “a fresh change of clothes’’ — several Cruz allies stoked rumors that Carson was dropping out.

“Carson looks like he is out,’’ tweeted Representative Steve King, a prominent Iowa Republican and one of Cruz’s top surrogates. “Iowans need to know before they vote. Most will go to Cruz, I hope.’’

King issued his tweet Monday as voters were streaming into precincts around the state and at about the same time the Cruz campaign sent out an e-mail to supporters.

“Breaking News. The press is reporting that Dr. Ben Carson is taking time off from the campaign trail after Iowa and making a big announcement next week,’’ it read. “Please inform any Carson caucus-goers of this news and urge them to caucus for Ted Cruz.’’

At some caucus sites, Cruz supporters spread rumors that Carson was dropping out. Some supporters showed up at a site where Rick Santorum was speaking and asked him to bring it up in his remarks. He declined.

“People are upset in Iowa about this,’’ said Craig Robinson, a former political director of the Iowa Republican Party who now runs an influential website, the Iowa Republican.

“There is substance here,’’ he added. “But in terms of the actual complaint, what do you do? I don’t know. . . . There’s nothing to my knowledge that allows you to challenge it.’’

The Iowa GOP on Wednesday night fully certified the results of the caucus.

Iowa’s secretary of state, Paul Pate, said he had no authority to oversee the party-run Iowa caucuses. “Any official challenge to the Iowa Caucus results would need to be done through the state and national political parties,’’ he said in a statement.

Cruz on Monday night won the Iowa caucuses, earning 28 percent of the vote to Trump’s 24 percent.

Senator Marco Rubio came in a strong third with 23 percent.

Carson, once a front-runner in Iowa, came in a distant fourth and blamed Cruz’s “deceit and dirty tricks and lies.’’

Cruz apologized in a statement on Tuesday, saying, “This was a mistake from our end, and for that I apologize to Dr. Carson.’’

Speaking with reporters on Wednesday, Cruz said his team had merely passed on to caucusgoers a CNN story about Carson going home to Florida, in an effort to encourage Carson supporters to back Cruz.

“It was breaking news that was relevant,’’ Cruz said, adding that the staffers involved will not be fired. “I would note that the news story we passed on was true and accurate. CNN reported it and, in fact, Ben did go to Florida instead of New Hampshire or South Carolina.’’

Trump seized on the issue on Tuesday night in a New Hampshire rally.

“He said Carson left Iowa. He’s out of the race, vote for him!’’ Trump said during the rally in Milford, N.H. “So Ben is all the sudden getting calls that he quit the race! These guys said, ‘He’s quit the race, he’s gone, he’s out! Send your votes to him.’ What kind of people are we dealing with, with these politicians?

“It’s honestly really, really dishonest,’’ Trump continued. “And I think I know why. You know why? Because he was born in Canada!’’

By Wednesday morning, Trump had escalated his characterization of the episode as “dishonest,’’ which attracted little media attention, to “fraud,’’ which instantly took off on social media.

Trump also objected to a flier that Cruz’s campaign sent out over the weekend before the caucuses.

The flier, made to look like it was a government document — with “VOTING ­VIOLATION’’ stamped at the top — graded Iowans for their past election turnout and said they needed to go to the caucuses to improve their scores.

Pate, the Iowa secretary of state, condemned the mailers but did not take further action against Cruz.

“Accusing citizens of Iowa of a ‘voting violation’ based on Iowa Caucus participation, or lack thereof, is false representation of an official act,’’ he wrote in a Facebook post.

“There is no such thing as an election violation related to frequency of voting. Any insinuation or statement to the contrary is wrong and I believe it is not in keeping in the spirit of the Iowa caucuses.’’

Matt Viser can be reached at matt.viser@globe.com.