Ivanka Trump, 34, is many things: a mother, an executive and an entrepreneur who has a prominent role in the Republican presidential campaign of her father, Donald J. Trump.

Now, because of comments by Mr. Trump and one of her brothers, she has been cast in perhaps an unfamiliar role: a central figure in a debate on social media about how a woman could — or should — respond to sexual harassment on the job.

The issue came up in an interview Mr. Trump had with USA Today that was published on Monday. A columnist asked him about comments he had made on “Meet the Press” on NBC about the sexual harassment case that led to the ouster of the powerful Fox News chairman and chief executive Roger Ailes.

Mr. Trump, who has himself faced strong criticism for his remarks about women — including derogatory and sexually charged comments about their bodies — said it was “sad” that former Fox News employees were “complaining” about being sexually harassed, and he appeared to question the truthfulness of their accusations.