Trump said he and Epstein fell out after he “stole” people who worked for him.
When asked specifically about Virginia Giuffre, Trump said “he stole her”.
Giuffre was aged 16 when she worked as a locker room attendant at Trump’s Mar-a-Lago club.
Her family issued a statement to NBC News in the wake of Trump’s remarks.
“It was shocking to hear President Trump invoke our sister and say that he was aware that Virginia had been ‘stolen’ from Mar-a-Lago,” the statement read.
“It makes us ask if he was aware of Jeffrey Epstein and Ghislaine Maxwell’s criminal actions, especially given his statement two years later that his good friend Jeffrey ‘likes women on the younger side … no doubt about it.’
“We and the public are asking for answers; survivors deserve this.”
The family also decried Trump after he refused to rule out pardoning Epstein’s accomplice Ghislaine Maxwell.
“The government and the president should never consider giving Ghislaine Maxwell any leniency,” the family said.
“Ghislaine Maxwell is a monster who deserves to rot in prison for the rest of her life for the extraordinary violence and abuse she put not just our sister Virginia through, but many other survivors, who may number in the thousands.”
Maxwell, another former friend of Trump, is serving a 20-year prison sentence for her role in the sex trafficking of minors.
Giuffre died by suicide at her farm in rural Western Australia in April this year.
She had made serious allegations against Epstein, Maxwell and Prince Andrew, who has denied any wrongdoing.
Giuffre later became an advocate for sex trafficking survivors.
Trump has been under pressure in recent weeks to release files relating to Epstein, though he has refused.
Trump is currently suing The Wall Street Journal after it reported claims he wrote a birthday message to Epstein which included a drawing of a naked woman.
The president has denied any wrongdoing in relation to Epstein.