In her lawsuit, Ms. Hughes said that Mr. Payne had “pressured” his way into her hotel room in July 2013 and coerced her to have sexual intercourse with him, even though she had refused his advances by telling him “no” and “stop.”

According to the suit, Ms. Hughes was “shocked and ashamed” and did not immediately report the episode. She said that over the next two years she was forced to engage in a sexual relationship with Mr. Payne. In exchange, she said, she received career opportunities, including increased appearances on Fox News and Fox Business and the promise that Mr. Payne would help her land a contributor contract, a job that can pay several hundred thousand dollars a year. Ms. Hughes never became a paid contributor at either channel.

Ms. Hughes, a regular guest on Fox News and Fox Business from 2013 through 2016, asserted that after she ended the relationship with Mr. Payne, the network blacklisted her. After she reported her allegations against him, she said, the network leaked a story to the news media about a romantic affair between Ms. Hughes and Mr. Payne.