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Robert F Kennedy Jr has apologised after a video was leaked of a private phone call in which Donald Trump is heard apparently trying to coax the independent presidential candidate to support him.

“I would love you to do something,” Trump can be heard saying in the clip. “And I think it’ll be so good for you and so big for you. And we’re going to win.”

Mr Kennedy then says: “Yeah.”

Trump and Mr Kennedy, a longshot third-party candidate, are political rivals who have occasionally criticised each other during the campaign.

The footage is said to have been recorded on Sunday, a day before the pair met in Milwaukee, Wisconsin, where the Republican convention is taking place, stoking speculation that Mr Kennedy might be about to exit the race and endorse Trump.

But Kennedy spokeswoman Stefanie Spear said on Monday that he was not dropping out.

Robert F Kennedy Jr posted on X on Tuesday: “When President Trump called me I was taping with an in-house videographer.

“I should have ordered the videographer to stop recording immediately. I am mortified that this was posted. I apologise to the president.”

It was Kennedy’s son, Robert F Kennedy III, who posted the footage online early on Tuesday.

The younger Kennedy said in the post on X, formerly Twitter, that he wanted to expose Trump’s “real opinion” on immunisations, but he swiftly deleted the clip.

Trump can also be heard in the video discussing discredited claims about the health risks of childhood vaccines, a longstanding concern for Mr Kennedy, but one which the scientific community has said is misinformation.

“I agree with you, man. Something's wrong with that whole system, and it's the doctors you find," Trump can be heard saying.

Also on Tuesday, Donald Trump Jr, the former president’s son, was asked about rumours that Mr Kennedy could join forces with the Republican presidential nominee.

Speaking at an event in Milwaukee, he said “maybe there’s a great place for him somewhere in an administration”.

Mr Trump Jr said he didn’t have any “inside scoop on that, certainly not now”, but he would “love to see that happen”.

Opinion polls suggest that Mr Kennedy could draw votes equally from Trump and the Democratic President Joe Biden, including in swing states, in this November's election.