Mr Mohamed, a British resident, claims he was tortured in US custody
The foreign secretary has declined requests to urge the US to publish documents about the alleged torture of freed detainee Binyam Mohamed.
David Miliband told MPs while he had "no objection" to publication it was up to the US to release any evidence.
Shadow foreign secretary William Hague had called for transparency, saying the UK could not be seen condoning torture.
Mr Mohamed, who arrived back in the UK on Monday, says he was tortured by US agents who suspected him of terrorism.
Mr Hague asked the foreign secretary: "The importance of this case is that this country must be clear that we do not condone or connive in the torture of suspects.
"Does that not suggest that we should be as transparent as possible in all the circumstances?"
But Mr Miliband said, while there was nothing in the documents that Britain wanted to be kept secret, "it was up to the US to go through each of those documents and decide whether or not to release them".
Earlier, a senior Labour MP called on the US authorities to "urgently" release details on Mr Mohamed, who says the British secret services were complicit in his abuse.
Mike Gapes, chairman of the Foreign Affairs Select Committee, told the BBC that there should be greater openness about Mr Mohamed's case to prevent long-term damage to the government and in particular, the reputation of the foreign secretary.
Mr Miliband has been accused by two senior judges of bowing to pressure from the US government to keep details of Mr Mohamed's treatment secret.
"I think the solution here is that the US authorities release that information," Mr Gapes said.
UK attorney general Baroness Scotland is also facing criticism for the length of time she is taking to decide whether to order a criminal investigation into Mr Mohamed's allegations about official British involvement in his torture.
Keith Vaz, chairman of the Home Affairs Select Committee, said: "She [Baroness Scotland] has access to the finest legal brains in Britain, including her own.
"To take four months to make a decision of this kind is a very long time. I think we need a decision now."
On Tuesday Mr Miliband released a statement repeating that the UK government "abhors torture and does not order or condone it", and that it had raised with the US allegations of mistreatment made by UK detainees held at Guantanamo Bay.
The BBC's security correspondent Gordon Corera said while it was clear that the High Court judges did believe Mr Mohamed had suffered some mistreatment, at the same time it was difficult to get to the truth because of the secrecy involved in intelligence sharing between Britain and the US.
Mr Mohamed arrived back at RAF Northolt in London on Monday
But our correspondent said court judgements did show there had been a transfer of information from the UK to America concerning Mr Mohamed's case.
Meanwhile Mr Mohamed, 30, is recovering from his seven years of detention - four of them spent at Guantanamo Bay - at a secret address in the countryside.
His sister Zuhra told the BBC that his weight had dropped from a "normal" 12 stones to 8st 10lb, but he was otherwise in good health, mentally and physically.
"He is happy, and glad to be out. He is just looking around. He is doing good and he can't believe he is free," she said.
Ethiopian-born Mr Mohamed's immigration status is being reviewed, but the authorities have stressed that allowing him to return to Britain does not confer on him permanent residency rights.
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