“He told me he has a number of friends who are affected,” Mr. Kennedy said of the conversation with the president-elect, describing 2-year-old children who had received “a battery” of vaccines and then exhibited a high fever followed by changes in behavior. “They all have the same story.”

Mr. Kennedy said Mr. Trump “believes in those anecdotal stories” about the dangers of vaccines. He said the president-elect “says if you have enough anecdotal stories saying the exact same thing, that you can’t dismiss the validity.”

He said a commission would probably last a year and be made up of “a mix of science people and other people hopefully from the media and other prominent Americans who hopefully don’t have a position going in.”

Mr. Kennedy wrote a book in 2014, “Thimerosal: Let the Science Speak,” arguing that a mercury-based preservative called thimerosal, found in vaccines, was responsible for causing autism in children. On his website, he accuses the Centers for Disease Control and Prevention of being a “cesspool of corruption, mismanagement and dysfunction” that has led the agency to overlook the affects of vaccines.

“With the research, regulatory and policy-making agencies captured, the courts closed to the public, the lawyers disarmed, the politicians on retainer and the media subverted, there is no one left to stand between a greedy industry and vulnerable children, except parents,” Mr. Kennedy wrote.

Such claims have been fueled over the past several years by social media, sometimes embraced by actors or fringe political candidates, often to the dismay of public health officials, who say the commentary is contrary to the facts.

The actress Kirstie Alley has written on Twitter that not all vaccines are harmless. Erin Brockovich, an environmental activist, wrote on the site in 2015, “I’ll be damned if any government is going to tell me what to put in my or kids’ bodies.” In 2011, Michele Bachmann, then a member of Congress from Minnesota and a Republican presidential candidate, called the vaccine to prevent cervical cancer “dangerous.”