•In a statement released Sunday a Democratic Party spokesman called Mr Kennedy "nothing more than a Trump stalking horse in this race".
•The ad was made by American Values 2024 political action committee, a Super Pac.
Robert F Kennedy Jr has apologised to relatives after a Super Bowl advert mirrored one broadcast by his uncle John F Kennedy's campaign in 1960.
Mr Kennedy, an environmental lawyer and anti-vaccine activist, is running for president as an independent.
The ad aired just before the Super Bowl halftime on Sunday.
It included images of Robert F Kennedy Jr spliced into the original 1960 ad, and a jaunty jingle that repeated the Kennedy surname 15 times in 30 seconds.
The ad was made by American Values 2024 political action committee, a Super Pac. Super Pacs are allowed to raise and spend an unlimited amount of money in support of political candidates, but cannot co-ordinate with campaigns.
The spot cost $7m (£5.5m), according to American Values 2024 co-founder Tony Lyons. One donor to American Values 2024 Pac, Tim Mellon, has given the group $15m. Mr Mellon is also a major donor to Pacs supporting Mr Trump.
One of Mr Kennedy's cousins criticised the advert and the candidate's anti-vaccine activism.
"My cousin's Super Bowl ad used our uncle's faces - and my Mother's. She would be appalled by his deadly health care views," Bobby Shriver, the son of Eunice Kennedy Shriver, President Kennedy's sister, wrote in a post on X. "Respect for science, vaccines, & health care equity were in her DNA."
In response, RFK Jr posted: "I'm so sorry if the Super Bowl advertisement caused anyone in my family pain. The ad was created and aired by the American Values Super PAC without any involvement or approval from my campaign. FEC rules prohibit Super PACs from consulting with me or my staff. I love you all. God bless you."
However, the advert remained pinned to the top of the candidate's X feed on Monday morning. Campaign spokeswoman Stefanie Spear told CBS News that the RFK Jr campaign was "pleasantly surprised and grateful to the American Values Pac for running an ad during the Super Bowl".
The original ad was an attempt to portray John F Kennedy as a balance of youth and experience. President Kennedy, a Democrat, was the youngest-ever elected president, and in 1960 was facing an experienced politician on the Republican side - incumbent Vice-President Richard Nixon.
The original included a catchy jingle with lines which were repeated in the recent Super Bowl ad: "Do you want a man for president who's seasoned through and through? A man who's old enough to know and young enough to do?"
Robert F Kennedy Jr is 70 years old - nearly three decades older than his uncle was in 1960. Yet he is younger than 77-year-old Donald Trump and 81-year-old Joe Biden, and voters have said they are concerned about the two candidates' ages.
Despite his name recognition, Mr Kennedy significantly trails Mr Biden and Mr Trump in polls. Research suggests his support hovers at around 10%.
Kyle Kondik, a political analyst at the University of Virginia's Center for Politics, said that the advertisement played on a theme common to many other Super Bowl ads: nostalgia.
"And remaking a political ad from the 1960s is about as nostalgic as you can get," he said.
"For any third party candidate, getting attention is part of the game, and this is a big political story today," Mr Kondik said. "He's also capitalising on the fact that he's an independent in a year where the public doesn't seem to like the two major party candidates very much... His last name is what he's got going for him."
Polls are mixed on whether Mr Kennedy's presence in the race might draw more support away from Mr Biden or Mr Trump - or attract voters who wouldn't have voted for either major party.
On Friday, Democratic Party leadership filed a complaint against the RFK Jr campaign with the Federal Election Commission, accusing it of co-ordinating too closely with American Values 2024 when it comes to efforts to get Mr Kennedy on the ballot in all 50 states.
In a statement released Sunday a Democratic Party spokesman called Mr Kennedy "nothing more than a Trump stalking horse in this race".