US Vice-President Joe Biden has spoken movingly about the death of his son Beau and says he is still unconvinced he could commit to a presidential run because of its effect on him.

He also revealed the centrality of his Catholic faith in helping him to cope with his bereavement.

Interviewed by Stephen Colbert on CBS's The Late Show, Biden – regarded by many obververs as a popular and credible alternative to Hillary Clinton for the Democratic Party nomination – was frank about the emotional toll Beau's death from brain cancer in May had taken on him.

He said that White House candidates had to be able to commit themselves fully to the task of the presidency and that he was unsure that he would be able to do so.

"I'd be lying if I said that I knew I was there," he said, adding: "Nobody has a right, in my view, to seek that office unless they're willing to give it 110 per cent of who they are. And I am, as I said, I'm optimistic, I'm positive about where we're going. But I find myself – you understand it – sometimes it just overwhelms you."

Biden also described details of conversations he had had with his son – himself a war veteran and rising political star before his death aged 46.

"He said, 'Dad, sit down, I want to talk to you.' He said, 'Dad, I know how much you love me,"' Biden recalled. "Promise me you'll be all right, because no matter what happens, I'm going to be all right."

However, he added that he felt "self-conscious" talking about his loss in the knowledge that others – including his host, who lost his father and two brothers in a plane crash as a child – had been through similar experiences. Biden himself lost his wife and infant daughter in a car crash at the start of his political career.

He referred to the "enormous sense of solace" that Catholic rituals give him. Biden revealed that he counts his rosary beads, used as an aid to prayer, and goes to mass.

"I go to mass and I'm able to be just alone, even in a crowd," he said.