Donald Trump said Thursday vaccine conspiracy theorist Robert F. Kennedy Jr. would be in charge of “women’s health” if the former president is reelected to the White House.

“He’s gonna work on health and women’s health and all of the different reasons,” Trump told supporters at a rally in Nevada. “Because we’re not really a wealthy or a healthy country … I told Bobby, ‘I want you to take care of health, I want you to look at the food and the food supply and what we put on the food.’”

The comments reflect Kennedy’s growing role in a potential administration and his rising standing in the Trump orbit after he dropped his independent bid for the presidency and endorsed his onetime competitor. But calls for a senior position have troubled health advocates, who point to Kennedy’s long history as a skeptic of widely accepted science surrounding vaccines. Those concerns grew this week after the co-chair of the team planning Trump’s potential transition said Kennedy had persuaded him in a 2.5-hour meeting that vaccines caused autism, a widely debunked stance.

The Harris campaign was quick to share footage of Trump’s plans for Kennedy on Thursday, and Harris herself tweeted a short response to her opponent’s pledge: “No.”

The effort builds on the vice president’s campaign to showcase Trump’s behavior toward women and his work to undue the landmark Roe v. Wade Supreme Court decision that protected access to abortion nationwide. Trump said at a separate rally on Wednesday that he would take steps to protect women once he is back in the White House “whether the women like it or not.”

“This is the same man who said women should be punished for their choices,” Harris told supporters in Arizona at her own event on Thursday. “He simply does not respect the freedom of women or the intelligence of women to know what’s in their own best interest and make decisions accordingly.”

“But we trust women.”

The Washington Post reported Thursday that Kennedy would likely have “significant” control over health and food safety in a new Trump administration, according to people familiar with internal discussions he has had with transition officials. That role could see him take on a position as a White House czar, the Post added, rather than the head of a cabinet department or agency that would require Senate confirmation.

“The president has asked me to clean up corruption and conflicts at the agencies and to end the chronic disease epidemic,” Kennedy told the Post on Wednesday. “He wants measurable results in two years and to return those agencies to their long traditions of gold-standard evidence-based science and medicine.”