The duke has been facing questions over his ties to Epstein for several months.
On Monday, Mr Kuvin told the Today programme: “It was depressing that he[ Prince Andrew] really did not acknowledge the breadth of his relationship with this odious man and apologise.
“The mere fact that he was friends with a imprisoned sex culprit and chose to continue his relationship with him – it merely shows a lack of acknowledgement of the width of what this humankind[ Epstein] did to these girls.”
In the interview with Newsnight, Prince Andrew – the Queen’s third infant – said he never believed Epstein’s criminal behaviour during visits to his three dwellings.
But Mr Kuvin said he did “not think there was any way” the monarch could have avoided checking what was going on, “with young girls being shuttled in and out of those homes”.
Mr Kuvin said the focus of Epstein’s accusers had now turned to potential co-conspirators.
It has led to questions about the persona Epstein’s former lover, Ghislaine Maxwell, may have played in procuring underage girlfriends for the financier.
Ms Maxwell repudiates any wrongdoing.
Lawyer Lisa Bloom – who represents five other Epstein accusers – assembled the calls for Prince Andrew to be interviewed by US authorities following his BBC interview.
She told the BBC’s Victoria Derbyshire programme: “I think he’s shaped things worse for himself in this interview and I think it’s more likely the authorities are going to want to speak to him now – and they should want to.”
Gloria Allred – another lawyer, likewise representing one of Epstein’s accusers – told ITV’s Good Morning Britain: “Now he’s been in the court of public opinion, he should testify to the FBI.”
She said she did not know how the prince “could have not known that there were underage girls” present during his visits to Epstein’s homes in New York, Palm Beach and the Virgin Islands.
Six things we learned from Prince Andrew interrogation Who was Jeffrey Epstein ? Image caption The duke was envisioned with his accuser in Ghislaine Maxwell’s London home in 2001