CAIRO — No one can say Melania Trump, the first lady, doesn’t understand the power of an image.

Standing in front of one of the best known but most enigmatic monuments of the ancient world, the Great Sphinx, Mrs. Trump — one of the most mysterious first ladies in modern times — agreed to take questions from a group of journalists.

Mrs. Trump — wearing another white hat — used the symbolic backdrop as a moment to discuss her six-day trip to Africa, including whether any of her hosts had brought up the disparaging comments her husband has reportedly made about African countries.

“Nobody discussed that with me,” she said of her hosts in Ghana, Kenya, Malawi and Egypt in the past week. Of the president, she added, “I never heard him saying those comments.”

When asked about Mr. Trump’s claim, made in response to the accusations of sexual assault against Brett Kavanaugh, that it was a “very scary time” for men, Mrs. Trump walked a line between saying victims needed to be heard and supporting Mr. Kavanaugh, whom she called highly qualified to join the Supreme Court.