Former President Donald J. Trump said on Sunday that he expected Robert F. Kennedy Jr. to have a “big role” in a second administration, and acknowledged the possibility that he could take action against two major public health successes — vaccines and the fluoridation of water — if he won the presidency.

The remarks, in an interview with NBC News, suggest that Mr. Kennedy, a former independent candidate, has assumed an elevated role in Mr. Trump’s orbit, and that Mr. Trump is keen, in the waning days of the presidential campaign, to appeal to a segment of his base that is deeply skeptical of such public-health interventions.

Mr. Kennedy has been a forceful surrogate for Mr. Trump on the campaign trail in recent weeks. In a call last week with supporters, Mr. Kennedy said that Mr. Trump had “promised” him control of the nation’s public health agencies, an assertion the Trump campaign called premature.

Mr. Trump, however, said at his recent rally in New York that he would let Mr. Kennedy “go wild on health,” and on Sunday Mr. Kennedy reiterated to Fox News that he was in talks with Mr. Trump about a high-level policy role. “I want to be in the White House, and he has assured me that I’m going to have that,” Mr. Kennedy said.

Mr. Kennedy asserted on Saturday that a second Trump administration would move swiftly to stop the fluoridation of drinking water. He is also a prominent critic of vaccines, particularly the childhood vaccination schedule, and has frequently claimed that some vaccines are linked to autism and other health issues, despite years of studies showing no such connection.

Mr. Trump’s remarks on Sunday about vaccines came in response to a question about whether “banning certain vaccines might be on the table,” given Mr. Kennedy’s opinions on the subject. Mr. Trump responded: “Well, I’m going to talk to him and talk to other people, and I’ll make a decision, but he’s a very talented guy and has strong views.”

Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.

Thank you for your patience while we verify access.

Already a subscriber? Log in.

Want all of The Times? Subscribe.