Prominent online personalities are joining Joe Rogan’s offer to donate thousands of dollars to charity if an American vaccine researcher agrees to appear on the podcasting behemoth’s show to debate Democratic presidential candidate Robert F. Kennedy Jr. about the safety and efficacy of Covid vaccines.

Mr. Rogan promised to donate $100,000 to charity if author Peter Hotez, a physician and researcher at Baylor University, would agree to come on his show to defend his assertion that Mr. Kennedy spread “misinformation” during an appearance on the Joe Rogan Experience podcast last week. On Saturday, the chief executive of Pershing Square Capital Management, Bill Ackman, said he would add $150,000 to the bounty.

Earlier, the owner of Twitter, Elon Musk, joined the online fray by suggesting that Mr. Hotez “is afraid of a public debate because he knows he is wrong.” Several other Twitter users less notable than Messrs. Musk and Ackman have also stepped up saying they would pitch in to help fund such a debate, bringing the total to more than $600,000 by Sunday.

So far, Mr. Kennedy has not responded publicly to the dust-up.

Dr. Hotez started the spat when he posted a critique of the episode of Mr. Rogan’s podcast Thursday that featured a three-hour interview with Mr. Kennedy. Mr. Hotez posted a link to an article in the now-bankrupt Vice magazine calling the episode “an orgy of unchecked vaccine misinformation” and a “detailed survey of Kennedy’s most dangerously incorrect views.”

“Spotify has stopped even sort of trying to stem Joe Rogan’s vaccine misinformation,” Dr. Hotez tweeted. “And from all the online attacks I’m receiving after this absurd podcast, it’s clear many actually believe this nonsense.”

Dr. Hotez, who has appeared on Mr. Rogan’s podcast in the past, later said he would be willing to have a “meaningful discussion” on the topic, but stopped short of accepting the challenge to debate Mr. Kennedy. He lamented that he was being “tag-teamed” by the Musk-Kennedy-Rogan trio, and pleaded with his critics to “remember what this is about — not a small number of Americans lost their lives from antivaccine disinformation during the pandemic.”

Mr. Kennedy, who is challenging President Biden for the Democratic presidential nomination and polling at between 15 percent and 20 percent among Democratic voters, has been a prominent critic of vaccines — not just Covid vaccines, but all vaccines — for decades. The 69-year-old son of the late Robert F. Kennedy, who was assassinated in 1968, he calls himself a “Kennedy Democrat” and is running on a platform emphasizing civil liberties, government transparency, and freedom from further health-related lockdowns.

Mr. Rogan has also grown increasingly skeptical of Covid vaccines on his show — the most popular podcast on the planet, with more than 10 million listeners — since the pandemic ended. He has been criticized for suggesting that young, healthy people do not need Covid vaccines and for platforming prominent critics of the mRNA technology behind the vaccines. His opinions so alarmed some health experts that they felt compelled to draft an open letter to Spotify, the platform on which his show airs, demanding that the company silence him.

“This is not only a scientific or medical concern; it is a sociological issue of devastating proportions and Spotify is responsible for allowing this activity to thrive on its platform,” the letter stated.