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“There is a reason why anybody has to swallow hard and think twice before participating in this media ecosystem,” Buttigieg said.

Still, the mayor of South Bend, Ind., said he thinks that many people who tune in to the network are doing so in good faith and that he wants to be willing to meet voters wherever they are.

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“There are a lot of Americans who my party can’t blame if they are ignoring our message, because they will never hear it if we don’t go on [Fox] and talk about it," Buttigieg said Sunday.

Buttigieg also took several opportunities to criticize President Trump, who earlier in the evening had tweeted his displeasure that his preferred news network was “wasting airtime on Mayor Pete.” When Wallace asked whether Trump should be impeached, Buttigieg said there was no question that Trump’s behavior was “beyond the pale, morally,” but he said it would be up to Congress to decide whether the president should be removed from office.

When Wallace asked how Buttigieg would handle Trump’s insults, attacks and tweets, the candidate started to respond before inhaling and trailing off.

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“The tweets are . . . I don’t care,” he said, to audience cheers.

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Buttigieg, a military veteran, also accused the Trump administration — in particular, national security adviser John Bolton — of “saber-rattling” at Venezuela and Iran at the risk of leading the United States into war.

In the wake of multiple states passing far-reaching antiabortion laws recently, Buttigieg also pushed back on Wallace’s questions about whether women should be allowed to terminate their pregnancies in the third trimester. He tried to avoid answering at first, saying he didn’t want to get into “hypotheticals” that were a setup.

When Wallace pointed out that his question wasn’t hypothetical, saying 6,000 women have third-trimester abortions each year, Buttigieg noted that that represented less than 1 percent of all women who have abortions, before responding specifically.

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“We’re talking about women who have perhaps chosen a name, women who have purchased a crib,” he said.

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Those women, he continued, probably had been expecting to carry their babies to term but had received medical news that forced them “to make an impossible, unthinkable choice.”

“The bottom line is, as horrible as that choice is — that woman, that family may seek spiritual guidance, they may seek medical guidance — but that decision is not going to be made any better, medically or morally, because the government is dictating how that decision is going to be made.”

Buttigieg’s campaign had held firm to its commitment to hold a town hall event on Fox News, which was scheduled before Warren publicly announced her decision to decline one. Other Democratic candidates have had mixed reactions to the network, which the Democratic National Committee has banned from taking part in primary debates.

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Fox News has held town hall events for Sens. Amy Klobuchar (D-Minn.) and Bernie Sanders (I-Vt.). Sen. Kirsten Gillibrand (D-N.Y.) will hold a town hall event on the network next month.

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On Sunday, the crowd at Stevens High School in Claremont, N.H., ultimately gave Buttigieg a rousing send-off at the end of his event, which seemed to surprise Wallace.

“Wow, a standing ovation,” the host said as they signed off.

Correction: An earlier version of this article incorrectly stated that Democratic presidential candidate Andrew Yang has held a Fox News town hall. Yang has appeared on the network several times, but none has been for a town hall event.