Ms. Trump’s suggestion that she be spared the question faced pushback online from journalists and others, who noted that she not only led the American delegation for the closing ceremony of the Olympics, but has also positioned herself as a voice for women’s issues inside the White House.

Some conservatives, in the meantime, suggested that her dismissal of the question was akin to one offered by Chelsea Clinton during the 2016 presidential campaign, when asked whether her father’s sex scandal had affected her mother’s credibility.

In the NBC interview, Ms. Trump also said that she had not yet been interviewed by Robert S. Mueller III, the special counsel investigating Russian interference in the 2016 election, but that she believed Mr. Mueller could be trusted. She also repeated the White House’s denials that her father’s presidential campaign had colluded with Moscow.

“Consistently we have said there was no collusion,” she said. “There was no collusion. And we believe that Mueller will do his work and reach that same conclusion.”