Greta Thunberg, the teenage climate activist from Sweden who delivered a much-watched speech at the United Nations on Monday, has been celebrated for her activism on climate change, including galvanizing the worldwide, youth-led protests of the last week. But she has also become a lightning rod, drawing attacks by television and social media commentators.

Fox News apologized after a pundit, Michael Knowles, called her “a mentally ill Swedish child” on one of its programs on Monday. (Ms. Thunberg, who is 16, has Asperger’s syndrome, a form of autism, and has called it “a superpower.”) The network called the comment disgraceful, and a spokeswoman said Fox had no plans to invite Mr. Knowles back.

Mr. Knowles, who writes for the conservative news site The Daily Wire, defended his remarks on Twitter, where he accused Ms. Thunberg’s supporters of exploiting her. The notion that she was being used as a puppet was repeated by others, including the conservative commentator Dinesh D’Souza.

The day before Ms. Thunberg’s United Nations speech, Mr. D’Souza likened her image to ones used in Nazi propaganda, posting a photo on Twitter of Ms. Thunberg, wearing her signature long braids, next to an illustration of a young woman with a similar hairstyle standing in front of a swastika flag.