The teenager condemned the president for the remarks as he insisted on Fox News that he is not a racist and supports the Black Lives Matter movement.
Mr Rittenhouse, 18, was asked by Carlson how he felt after people like the US president had linked him to white supremacists in the wake of the Kenosha riots and his arrest for killing two protesters and injuring another.
“Mr President, if I can say one thing to you, I would urge you to go back and watch the trial and understand the facts before you make a statement,” Rittenhouse said.
“It is an actual malice and defaming my character for him to say something like that.”
The teenager added that it was “sickening” and a “disgrace” for people to have spread lies about his case.
Mr Biden used the phrase “white supremacist” in September 2020 following the presidential debate in which Donald Trump refused to condemn right-wing violence, infamously telling the Proud Boys to “stand back and stand by”.
“There’s no other way to put it: the President of the United States refused to disavow white supremacists on the debate stage last night,” Mr Biden tweeted.
During the interview Mr Rittenhouse, who told Carlson he now wanted to become a nurse or lawyer, said that his case had never had anything to do with race.
“To be honest this case has nothing to do with race, it never had anything to do with race, it had to do with the right to self-defence,” he said.
“I am not a racist person I support BLM, I support peacefully demonstrating, I believe there needs to be changes, I believe there is a lot of prosecutorial misconduct, it is amazing to see how much a prosecutor can take advantage of people.”
And he told Carlson that he believed the jury reached the right decision in acquitting him on all charges last week.
“I thought they came to the right verdict. It was not Kyle Rittenhouse on trial in Wisconsin, it was the right to self- defence on trial,” he added.
He also said he was aware of the threats being made against him, and was asked if he thought the “government” would protect him.
“I hope so, but we all know how the FBI works,” he said with a smirk.
Before the interview started, Carlson described Mr Rittenhouse as a “bright, decent, dutiful and hard working” person, who had “wanted to keep violent lunatics from setting fire to cars.”
“It’s hard to ignore the yawning class divide between Kyle Rittenhouse and his many critics in the media. Rittenhouse comes from the least privileged sector of our society,” he added.
In a preview of Carlson’s documentary on the case, Mr Rittenhouse said that he has vivid dreams about what happened in Kenosha, and many ended in his death.
Kyle Rittenhouse said he has dreams every night following the shootings.
“I’m alive but what could have happened,” Mr Rittenhouse said.
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