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Jeb Bush told a crowd in South Carolina on Thursday that Republicans could attract more African-Americans with a message of “hope and aspiration,” and not with promises of “free stuff” — a phrase that echoed comments made by Mitt Romney during and after his 2012 bid for president.

The remarks, first reported by The Washington Post, came in response to a question from a white man in a largely white crowd in Mount Pleasant, who asked how Mr. Bush planned to appeal to African-Americans.

“Our message is one of hope and aspiration,” Mr. Bush said. “It isn’t one of division and get in line and we’ll take care of you with free stuff. Our message is one that is uplifting — that says you can achieve earned success.”

While Mr. Bush has spoken often of broadening the party’s appeal, he has stumbled at times while attempting to deliver the message.

A spokeswoman for Mr. Bush, Kristy Campbell, noted that the candidate “talks constantly about the need for Republicans to reach out to all voters,” though she did not directly address the reference to “free stuff.”

“We will never be successful in elections without communicating that conservative principles and conservative policies are the only path to restoring the right to rise for every single American,” Ms. Campbell said.

The Bush campaign also said that while the question posed to Mr. Bush alluded specifically to black voters, his response broadened the context to voters across the board.

Mr. Bush’s wording called to mind a handful of uncomfortable moments from Mr. Romney’s 2012 campaign.

In a speech after being booed at an earlier event with the N.A.A.C.P., Mr. Romney, according to a pool report, said, “Your friends who like Obamacare, you remind them of this: If they want more stuff from government, tell them to go vote for the other guy — more free stuff. But don’t forget nothing is really free.”

And on a conference call with donors days after the election, Mr. Romney attributed his loss in part to policy “gifts” that the president had bestowed upon traditional Democratic constituencies, including African-Americans and Hispanics.

Mr. Bush’s broader message on Thursday — on the need, generally, to find ways to appeal to groups that have not been inclined to support Republicans recently — was consistent with many of his past remarks.

In many ways, Mr. Bush would appear to be among the most natural bridges to African-American and Latino voters in the Republican field — a candidate with a Mexican-born wife and a history of outreach to African-Americans during his campaigns for Florida governor, at least at times.

In his remarks on Thursday, Mr. Bush also made an unsubtle dig at Donald J. Trump, who recently criticized him for answering questions in Spanish.

“If someone asks me a question, just for the record, don’t take offense that I answer in Spanish,” Mr. Bush said. “It’s not an offense to you. It’s a respect for others.”

He reiterated the need to “campaign in a way that draws people toward your cause.”

It is an ambition he has long grappled with, particularly with African-American voters. During a debate in 1998, Mr. Bush showed remorse when asked about his relationship with the state’s black voters, who had flocked to his opponent four years earlier. “Republicans have ignored the black vote in this state, and I was part of that, and it was a mistake,” Mr. Bush said.

But in the early months of his run for the White House, Mr. Bush has found ways, presumably unintentionally, to alienate certain groups. Perhaps most memorably, he defended his use of the phrase “anchor baby” by arguing it was “more related to Asian people.”

Hours after the comments on Thursday, the campaign highlighted his frequent discussion of the need for widespread outreach, contrasting Mr. Bush with President Obama, who the campaign said had “worked to divide Americans for political gain.”

“His focus is on uplifting people, not dividing them,” Ms. Campbell, the spokeswoman, said of Mr. Bush, “and that is a message he will take across America.”