Nikki Haley, battling attacks from Donald J. Trump that she is too liberal and accusations from Ron DeSantis that she has been hiding from voters and reporters, hit back on Thursday, taking questions and defending her conservative credentials.

“This is the problem with the Republican Party now — they want to go and push everybody away that doesn’t fit their narrative,” she told reporters in Hollis, N.H, when asked about messaging from her opponents painting her as in the pocket of Democratic donors. “I have said it to the Republican Party over and over again — we have lost the last seven out of eight popular votes for president because you keep pushing people away.”

Asked about Mr. Trump’s plans to argue that nominating her for the White House would cost Republicans all the way down the ballot, Ms. Haley told reporters that “Americans aren’t stupid.”

“The reality is, who lost the House for us? Who lost the Senate? Who lost the White House? Donald Trump. Donald Trump. Donald Trump,” she said.

The back-and-forth appeared to be a dry run for her CNN town hall Thursday night, days before the New Hampshire primary next week. It was also a rare moment for Ms. Haley on the trail.

Ms. Haley, 51, the former governor of South Carolina and a United Nations ambassador under Mr. Trump, has run a tightly controlled campaign. Though she has held hundreds of events in the early voting states of Iowa, New Hampshire and South Carolina, she has held roughly a half-dozen news conferences since August, including “gaggles,” where the reporters following her on the trail are able to ask questions.

In recent weeks, she had stopped taking questions from voters at her events in Iowa and New Hampshire, frustrating some attendees, particularly in New Hampshire, where voters tend to want to hear from candidates and weigh their ballot decisions until the very end.

Mr. DeSantis, her top rival for second place, has seized on that sense of remove, with his campaign referring to her as a “bubble-wrapped candidate” in a recent email blast.

“Try as she might, you cannot try to hide your way to this nomination — and Nikki Haley is continuing to be exposed for caving to the left on every issue that is important to conservatives,” said the email, sent by Andrew Romeo, the campaign’s communications director.

On a conservative radio program, “The Hugh Hewitt Show,” on Thursday morning, Mr. DeSantis criticized Ms. Haley for refusing to debate after she announced this week that she would no longer participate in primary debates that don’t include Mr. Trump. With a large lead in most polls, the former president has skipped every primary debate so far.

“I’m the only one that’s not at this point running a basement campaign,” he argued on the show. “Biden’s running a basement campaign. Trump won’t debate, won’t take questions from voters. And now, Haley won’t debate and won’t take questions from voters.”

At recent events in New Hampshire, some voters have raised concerns that her refusal to engage with audiences could hurt her chances there. Several wondered whether the decision came after the wave of negative press Ms. Haley received in December when a voter asked her to explain the causes of the Civil War and she failed to mention slavery.

Nelia Tefft, an unaffiliated voter from Center Conway, N.H., who drove two hours through a snowstorm to attend her Monday rally in Bretton Woods, said she was surprised Ms. Haley did not take questions as she had in her previous events, before she rose in the polls.

“Then she was there forever taking pictures with people,” she said of Ms. Haley. “I was a little disappointed. I like to see her in action, answering off the cuff and she does it well most of the time, except for the Civil War, I guess.”

Ms. Haley’s schedule until Thursday had been light, with only one public event a day. Her plans for the stump in New Hampshire took a slight detour on Tuesday night when she flew back to South Carolina after her father, Ajit Singh Randhawa, who has cancer, was hospitalized, a campaign spokeswoman confirmed. He was reportedly in stable condition.

For the most part, the small and insular nature of Ms. Haley’s campaign has helped earn a reputation as a disciplined operation. Her top advisers tend to shun journalists, and her campaign officials and allies argue that — unlike the campaigns of her opponents — Ms. Haley’s has not been troubled by leaks.

But in Rochester, N.H., on Wednesday night, Gov. Chris Sununu of New Hampshire, who has endorsed her, attempted some damage control. He contended that her decision to cut the questions would not hurt her with his state’s voters and that she had done so because she wanted to spend more time “taking selfies” and shaking hands one-on-one, he said.

“People come up all the time asking her questions,” he said.

In Hollis, N.H., on Thursday morning, Ms. Haley took three questions from the audience of more than 200 people that allowed her to respond to some of Mr. Trump’s frequent attacks on her. .

She shot back at Mr. Trump’s attacks on her record and again warned voters he was the reason Republicans had “lost the midterms.”

“In five days we shock the country,” she said.

Afterward, she told reporters that she was not concerned about Mr. DeSantis overtaking her in her home state, South Carolina, as he has moved much of his staff there. “We are focused on Trump,” she said.

But asked whether Mr. Trump was still qualified to be president if he was convicted, she dodged. “It’s more than that — do you think the American people are going to vote for someone who has been convicted?” she asked, saying they were more worried about the economy, education and the state of the world. “I am going to beat him so we don’t ever have to deal with, ‘Are we going to elect a convicted felon?’”

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