“I have the answer, and it’s not right,” he said.
“That’s what I would say to anybody who would give me the answer.”
The two men met through an internet forum.
“It’s a bit embarrassing that it’s come out this way,” he added.
Mr Trump said he would not have met Mr Biden had he not been a lifelong Democrat.
“You know I’m not going to give him an answer,” Mr Trump said of Mr Biden.
The US President-elect said Mr Biden would not be his running mate.
He has not commented on the allegation that he met Mr Pence on the campaign trail.
However, Mr Trump has repeatedly attacked Mr Pence for supporting the Iraq war and has denied the allegation.
According to the AP, Mr Biden said he was disappointed that Mr Trump had chosen him to be his vice president.
During a campaign stop in Iowa on Saturday, Mr Pence said Mr Trump was a man of integrity and that the former Republican candidate had not done anything wrong.
“I think that he is a person who is going to be able to get things done, but I’m going to make sure that when he takes office he’s going to put his country first, because I’m a conservative and a man who believes that every American has the right to live in dignity,” Mr Pence told a crowd.
Former President Barack Obama, a Democrat, has denied Mr Trump made the claim, while Republican Sen Ted Cruz of Texas has called Mr Trump’s allegation “a joke”.
“I don’t believe it,” Mr Cruz told ABC News on Sunday.
After the election, Mr Obama said Mr Pence had not made the allegation, which has become a touchstone of the Republican Party, because he had been briefed on the matter and did not recall it. ABC/wires