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MERRIMACK, N.H. – Jeb Bush, whose wife is Mexican and three children were raised to celebrate their bicultural roots, showed a flash of anger on Saturday as he said that he “absolutely” took personal offense when Donald Trump recently described Mexican immigrants coming to the United States as “rapists” and criminals.

Mr. Bush, a former Florida governor, used his strongest language yet to denounce Mr. Trump, a rival for the 2016 Republican presidential nomination and the second-place finisher behind Mr. Bush in a New Hampshire poll that was conducted after Mr. Trump made those remarks. Mr. Bush, after marching in an Independence Day parade here with two of his children, George and Noelle, said that Mr. Trump’s views are “way out of the mainstream” of the party.

“To make these extraordinarily ugly kind of comments is not reflective of the Republican Party,” Mr. Bush said about Mr. Trump, whose comments caused NBC, Univision, Macy’s and others to cut ties with him.

“He’s doing this — he’s not a stupid guy, so I don’t assume he thinks that every Mexican crossing the border is a rapist. He’s doing this to inflame and incite and to draw attention, which seems to be the organizing principle of his campaign,” Mr. Bush said.

Asked if he took Mr. Trump’s remarks personally, given his family, Mr. Bush became a little cross.

“Yeah, of course it — absolutely — and a lot of other people” did as well, he said. “But politically, we’re going to win when we’re hopeful and optimistic and big and broad rather than errrrr, grrrr, just angry all the time. This is an exaggerated form of that, and there is no tolerance for it.”

Another Republican candidate, Gov. Chris Christie of New Jersey, gave a different answer on Friday when asked about Mr. Trump, a longtime friend. He criticized Mr. Trump’s remarks but then appeared to vouch for him.

“I like Donald. He’s a good guy,” Mr. Christie said. “And as I said right from the beginning, he’ll be as serious a candidate as he wants to be. Those are his choices.”

Mr. Trump issued a statement in response to the criticism, saying, “Today, Jeb Bush once again proves that he is out of touch with the American people. Just like the simple question asked of Jeb on Iraq, where it took him five days and multiple answers to get it right, he doesn’t understand anything about the border or border security. In fact, Jeb believes illegal immigrants who break our laws when they cross our border come “out of love.” ”