At a rally for seniors in Fort Lauderdale, Florida, on Friday, President Trump took aim at Mr Biden and his son.
Mr Trump said: “Does anybody know a middleman? It’s Biden’s son, it’s Hunter,” before moving away from the microphone as the crowd cheered.
“I bet Hunter is a middleman, he’s like a vacuum cleaner, he follows his father around collecting ... what a disgrace, it’s a crime family,” the president added, without citing any evidence.
“You want to know something? It’s a crime family, he’s following in his father. Hunter Biden is a middleman … Hunter made no money until he father became vice president and now he’s like a vacuum cleaner," Mr Trump claimed.
The president was referring to an article published in the New York Post earlier this week that alleged the Democratic presidential nominee might have met with an adviser to the board of Ukrainian energy company Burisma, while Hunter was on its board.
On Tuesday, the Post claimed that a repairman from Delaware had acquired an unverified cache of documents that revealed that the Democratic presidential nominee might have been willing to hold a meeting with Burisma adviser Vadym Pozharskyi at the time that Mr Biden led policy on Ukraine for the Obama administration.
The Biden campaign swiftly responded to the claims and told Politico: “The New York Post never asked the Biden campaign about the critical elements of this story.
“Moreover, we have reviewed Joe Biden's official schedules from the time and no meeting, as alleged by the New York Post, ever took place.”
Questions were raised about the veracity of the story when it emerged that Rudy Giuliani, Mr Trump’s personal lawyer, and Steve Bannon, the president’s former adviser, were involved in giving it to the paper. Mr Giuliani spent months in Ukraine trying to dig up dirt on Hunter Biden.
Facebook limited the spread of the article on its platform, while Twitter blocked users from tweeting out the link to the story and from sending it in private messages, as part of the social media platform’s misinformation polices. Republicans have claimed that the tech giants’ actions constitute censorship.
Republicans have repeatedly attempted to find evidence of corruption by the Democratic nominee, but have so far not found any to support their claim that US foreign policy was influenced by Hunter’s position at Burisma.
Mr Trump was impeached by House Democrats in 2019 for threatening to withhold military aid to Ukraine, if the country did not investigate Hunter’s employment at the energy company. He was cleared by GOP allies in the Senate.
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