Mr Trump took to Truth Social to defend himself and claimed he had deliberately mistaken Mr Biden for Mr Obama to show that “others” may have a “very big influence” in running the country.
“Whenever I sarcastically insert the name Obama for Biden as an indication that others may actually be having a very big influence in running our Country,” Mr Trump wrote in the post on Monday.
“Ron DeSanctimonious and his failing campaign apparatus, together with the Democrat’s Radical Left ‘Disinformation Machine,’ go wild saying that ‘Trump doesn’t know the name of our President, (CROOKED!) Joe Biden. He must be cognitively impaired.”
And he added: “No, I know both names very well, never mix them up, and know that they are destroying our Country.”
Mr Trump’s denial came as Forbes reported that the 77-year-old Republican had mixed up their names seven times in the past several months.
During a speech in New Hampshire, Mr Trump said he had watched an interview of Hungarian Prime Minister Viktor Orban, and claimed the politician had been asked “What would you advise President Obama? The whole world seems to be exploding.”
During a rally in Iowa on 1 October, Mr Trump referred to Mr Obama when he meant Mr Biden, and did the same thing twice in an 11 October interview on Fox News Radio.
He also made the same mistake three times during a 15 September speech before a faith summit in Washington DC.
Mr Trump’s 2024 rivals have picked up on the mistakes, with the DeSantis War Room account on X posting a string of the gaffes.
“Trump has been having serious trouble with names lately. On a number of occasions, he’s confused Obama and Biden. Here’s a really concerning moment,” the account stated.
In response, Mr Trump has said that he “Aced” a cognitive test as part of his latest medical exam.
Mr Biden, 81, is the oldest ever US president and would be 86 at the end of his second term if he wins in 2024.