"If you have relevant information you should be prepared to share it", he said after the former prince ignored a request to testify.
The Prime Minister declined to comment on the disgraced former royal specifically, but said as a "general principle" anyone with relevant details should be prepared to disclose them.
US legislators have criticised Andrew for what they described as "silence" amid their investigation into pedophile financier Epstein, who took his own life in a New York prison in 2019 while awaiting trial on sex trafficking and conspiracy charges.
Members of the House Oversight Committee had requested a "transcribed interview" with the former prince in connection with his "long-standing friendship" with Epstein.
But after saying they had not heard from him, Democrats Robert Garcia and Suhas Subramanyam accused Andrew of hiding.
Asked whether Andrew should help the probe, Sir Keir told reporters at the Johannesburg G20 summit: "I don't comment on his particular case.
"But as a general principle I've held for a very long time is that anybody who has got relevant information in relation to these kind of cases should give that evidence to those that need it.
"That would be my general position on this."
Pressed on whether that would apply to Andrew, he said: "In the end that will be a decision for him.
"But my general position is, if you have relevant information you should be prepared to share it."
Andrew, who was stripped of his prince and Duke of York titles earlier this month, denies any wrongdoing.
He was banished from the monarchy and busted down to a commoner by his brother the King because of his "serious lapses of judgment" over his association with convicted sex offender Epstein.
The move followed the publication of the late Virginia Giuffre's posthumous memoirs - who had accused him of sexually assaulting her when she was a teenager - and the US government's release of documents from Epstein's estate.
The Metropolitan Police is looking into claims Andrew passed Giuffre's date of birth and social security number to his taxpayer-funded bodyguard in 2011 and asked him to investigate.
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