Starmer said he had not known about the strength of the relationship between Mandelson and Epstein when he appointed him to the role in December, 2024.
Starmer has previously said he will release the vetting advice he was given when he selected Mandelson for the Washington role, but on Thursday he said he also needed to abide by a police request not to release anything that could prejudice an investigation.
"It had been publicly known for some time that Mandelson knew Epstein, but none of us knew the depth and the darkness of that relationship," he told reporters.
"I want to say this (to the victims): I am sorry. Sorry for what was done to you, sorry that so many people with power failed you, sorry for having believed Mandelson's lies and appointing him."
On Wednesday, Starmer gave way to a demand by the opposition Conservatives that the government publish information on how Mandelson was appointed.
But he sought to narrow the scope of documents to be released, saying he would not publish any that could be prejudicial to national security or international relations.
Mandelson, a government minister when Starmer's Labour Party was last in power more than 15 years ago, quit the House of Lords on Tuesday over links to Epstein, and is now under police investigation for alleged misconduct in office.
Files released by the US Justice Department last week include emails suggesting Mandelson had leaked government documents to Epstein, and that Epstein had recorded payments to Mandelson or his then-partner, now husband.
Mandelson has said he does not recall having received payments.
He has not commented publicly on the allegations he leaked documents, and did not respond to messages seeking comment.
Starmer defended his own response, saying he had moved quickly to strip all titles and roles from a man he accused of "betraying" the United Kingdom.
Starmer appointed Mandelson in late 2024, arguing that Mandelson's past work in the governments of Tony Blair and Gordon Brown and as the European Union's trade commissioner made him an ideal person to navigate relations with the US under President Donald Trump.
Starmer sacked Mandelson in September after seven months in the job, when documents emerged showing he had remained close to Epstein after the financier was found guilty in 2008 of child sex crimes.
Emails released last week appeared to indicate that in 2009 Mandelson sent Epstein a memo written for Brown about possible UK asset sales and tax changes, and in 2010 gave Epstein advance notice of a 500-billion-euro ($A839 billion) bailout by the EU.
On Tuesday, Starmer's government passed a dossier about Mandelson to police, who launched an investigation into Mandelson over alleged misconduct in public office.
Other messages in the US files appeared to show Mandelson celebrating Epstein's release from jail as "Liberation day" and how they exchanged sleazy jokes.
One email thread from July 2009 apparently shows the then-government minister asking Epstein how they should celebrate his release from prison after serving 13 months for soliciting prostitution with a minor.
Epstein responded: "With grace and modesty (those are the names of two strippers)."
Mandelson said: "From now on, grace and modesty sd be discovered in London."
Mandelson reportedly told the Daily Mail the messages were his but "they are his (Epstein's) observations not mine" and that he was saying Epstein "should find grace and modesty not strippers".
The 2009 emails also show Mandelson asking "How is freedom feeling?", to which the sex offender replied: "she feels fresh, firm, and creamy".
"Naughty boy," Mandelson wrote in response.
In another message Lord Mandelson can be seen telling Epstein upon his release: "Liberation day ! X."
The crude messages have prompted disgust from political figures, with SNP Westminster leader Stephen Flynn writing on X: "Sick bastards."
with PA
