The ex-wife of the Duke of York's email to Epstein, dated April 26, 2011, came weeks after she told reporters she would "never have anything to do with" the sex offender again.
The message, reported by The Sun newspaper, showed the duchess "humbly apologised" to Epstein for linking him to pedophilia in the media, labelling him "steadfast" and "generous".
It was sent "in the context of advice the duchess was given to try to assuage Epstein and his threats", her spokesman said.
The duchess's interview with the Evening Standard on March 7, 2011, saw her apologise for accepting Stg15,000 ($A31,011) from Epstein.
"I abhor pedophilia and any sexual abuse of children and know that this was a gigantic error of judgment on my behalf. I am just so contrite I cannot say," she said.
"Whenever I can, I will repay the money and have nothing ever to do with Jeffrey Epstein ever again."
A month later, the duchess sent an email from her private account to the sex offender, apologising.
"I know you feel hellaciously let down by me," her message read.
"And I must humbly apologise to you and your heart for that.
"You have always been a steadfast, generous and supreme friend to me and my family."
"I am apologising to you today for not replying to your email or reaching out to you. I was bedridden with fear. I was paralysed," she wrote.
"I was advised in no uncertain terms, to have nothing to do with you and to not speak or email you.
"And if I did - I would cause more problems to you, the Duke and myself. I was broken and lost.
"I didn't want to hurt Andrew one more time. I was in over-riding fear. I am sorry."
The duchess's spokesman said Epstein had threatened to sue her for defamation after associating him with pedophilia.
"The duchess spoke of her regret about her association with Epstein many years ago, and as they have always been, her first thoughts are with his victims," the spokesman said.
"Like many people, she was taken in by his lies," he said.
"As soon as she was aware of the extent of the allegations against him, she not only cut off contact but condemned him publicly, to the extent that he then threatened to sue her for defamation for associating him with pedophilia.
"She does not resile from anything she said then.
"This email was sent in the context of advice the duchess was given to try to assuage Epstein and his threats."
Epstein was found dead in his cell at a federal jail in Manhattan in August 2019 while awaiting trial on sex-trafficking charges.
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