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FORT MILL, S.C. — Disparaging Donald J. Trump’s temperament, questioning his beliefs and even knocking his polling numbers, Senator Ted Cruz of Texas laid into Mr. Trump in earnest on Saturday and abandoned any reluctance to take on his popular Republican rival.

It was a remarkable turn for a candidate who, less than a week ago, was resisting opportunities to tweak Mr. Trump even as he raised questions about Mr. Cruz’s eligibility for the presidency because of his Canadian birth.

“Donald’s record does not match what he says in the campaign,” Mr. Cruz told reporters before a national security forum here, two days after the debate that amplified their feud.

The remarks came hours after a characteristic early-morning flurry of tweets from Mr. Trump in which he attacked Mr. Cruz over his place of birth and his ties to Goldman Sachs, among other subjects. Mr. Cruz’s wife, Heidi, is a managing director in Goldman Sachs’s Houston office (she is on leave during the campaign), and during his Senate race in 2012 he obtained a loan from Goldman Sachs that he did not properly disclose.

Ted Cruz said he "didn't know" that he was a Canadian Citizen. He also FORGOT to file his Goldman Sachs Million $ loan papers.Not believable — Donald J. Trump (@realDonaldTrump) January 16, 2016

Was there another loan that Ted Cruz FORGOT to file. Goldman Sachs owns him, he will do anything they demand. Not much of a reformer! — Donald J. Trump (@realDonaldTrump) January 16, 2016

The Ted Cruz wiseguy apology to the people of New York is a disgrace. Remember, his wife's employer, and his lender, is located there! — Donald J. Trump (@realDonaldTrump) January 16, 2016

“It seems Donald has a lot of nervous energy,” Mr. Cruz said. “And for whatever reason, Donald doesn’t react well when he’s going down in the polls.” (Mr. Cruz has moved into a virtual tie with Mr. Trump in some Iowa polls, but Mr. Trump continues to lead the race in national polling.)

Then Mr. Cruz offered a Trumpian flourish — citing a recent poll that showed him beating Mr. Trump head to head — before taking aim at Mr. Trump’s disposition.

“I think in terms of a commander-in-chief, we ought to have someone who isn’t springing out of bed to tweet in a frantic response to the latest polls,” Mr. Cruz said.

He also sustained his tussle with Mr. Trump over “New York values,” the term Mr. Cruz has used in recent days, including during Thursday night’s debate, to define the developer’s background.

It is a fight Mr. Cruz’s campaign clearly relishes. Since Friday, when Mr. Cruz offered a faux apology to New Yorkers who he said were suffering under liberal policies, Cruz aides and allies have repeatedly circulated his comments.

On Saturday, Mr. Cruz said it was “curious” that Mr. Trump had aligned himself with left-leaning officials in New York in calling for the apology.

“It does raise the question of, O.K., if you are offended at my pointing out how much the failed policies have hurt New Yorkers, then which of those policies do you agree with?” Mr. Cruz said.

He added that, because Mr. Trump had donated to Hillary Clinton and Gov. Andrew M. Cuomo, “it’s a fair inference that he supports their policies.”

Later, Mr. Cruz’s campaign sent reporters a video of an interview with Mr. Trump from 1999, when he said on “Meet the Press” that he was “very pro-choice” and that he was more likely to support gay rights because he lived in New York.

“It is a little bit curious that he is now offended at the notion that he embodies New York values,” Mr. Cruz said.

Mr. Cruz acknowledged that Mr. Trump had begun to sound “fairly conservative” on the campaign trail, but he said voters were “far more discerning.”

Moments later, Mr. Cruz ended his news conference and entered an elevator, which briefly became stuck.

“So,” he said when he emerged, “who put Donald Trump in charge of the elevators?”