Donald Trump has falsely claimed not to know the Duke of York as pressure rises on the latter to submit to questioning in America over his links to the sexual abuser Jeffrey Epstein.

The US president was asked during an event at the US ambassador’s residence in London on Tuesday about the Queen’s son having stepped down from royal duties after his disastrous BBC interview about the allegations. “I don’t know Prince Andrew, but that’s a tough story, it’s a very tough story,” he answered.

Facebook Twitter Pinterest Donald Trump with his future wife, Melania, and Prince Andrew at the Mar-a-Lago estate on 12 February 2000. Photograph: Davidoff Studios Photography/Getty Images

In reality, he has met the prince on numerous occasions. The two have been pictured together at various events, including a party at Trump’s Mar-a-Lago resort on 12 February 2000, at which Trump was also separately pictured with Epstein.

The president has referred to the convicted sex offender, who took his own life in jail in August, as a “terrific guy” and “a lot of fun to be with”. Trump has himself denied numerous accusations of sexual abuse by different women.

Lawyers for five women who have accused Epstein of abusing them have called upon Andrew to give evidence about what he knows, saying he could have important information about trafficking for sexual abuse.

The prince has consistently and categorically denied the allegations, which Buckingham Palace said were “false and without foundation”. He has said he regrets maintaining relations with Epstein after his conviction for sexual offences.

Play Video 1:04 Virginia Giuffre: Prince Andrew's accuser asks Britain to 'stand beside her' – video

One of Epstein’s victims, Virginia Giuffre, alleges that she was trafficked to have sex with Andrew on three occasions between 2001 and 2002, on the instructions of Ghislaine Maxwell, a socialite and friend of both Epstein and the prince.

In an interview with the BBC’s Panorama programme that was broadcast on Monday, Giuffre said: “This is not some sordid sex story. This is a story of being trafficked. This is a story of abuse and this is a story of your guy’s royalty.”

Giuffre said it was a “wicked” and “scary” time in her life. “I had just been abused by a member of the royal family.”

She added: “I just didn’t expect it from royalty. I didn’t expect it from someone that people look up to and admire in the royal family … I couldn’t comprehend how the highest levels of the government, powerful people, were allowing this to happen, not only allowing it to happen but participating in it.”