Binyam Mohamed says he was tortured while in custody
The White House has expressed "deep disappointment" at a UK court ruling that information on the alleged torture of a UK resident had to be disclosed.
A spokesman added the judgement would "complicate" intelligence sharing.
Foreign Secretary David Miliband lost an Appeal Court bid on Wednesday to prevent the details being published.
Ethiopian-born Binyam Mohamed, 31, says UK authorities knew he was tortured at the behest of US authorities after his detention in Pakistan in 2002.
The ruling led to the publication of a summary of the torture of Mr Mohamed.
The information had been given to MI5 by the CIA - and suggested that British officials were aware of Mr Mohamed's ill-treatment.
Mr Miliband had repeatedly tried to stop its publication on the grounds that it could damage intelligence-sharing with America.
US Secretary of State Hilary Clinton is believed to be "understanding" about the UK government's position after talking with Mr Miliband, the BBC has learned.
But Ben LaBolt, a spokesman for President Barack Obama, said: "We're deeply disappointed with the court's judgment because we shared this information in confidence and with certain expectations.
"As we warned, the court's judgment will complicate the confidentiality of our intelligence-sharing relationship with the UK, and it will have to factor into our decision-making going forward."
The Federal Government is closed because of blizzard conditions and it is thought it will take some time for the American government to work out the implications of the lengthy judgement.
Denis Blair, the US Director of National Intelligence, said: "The decision by a United Kingdom court to release classified information provided by the United States is not helpful, and we deeply regret it.
"The United States and the United Kingdom have a long history of close co-operation that relies on mutual respect for the handling of classified information."
Judges ruled that paragraphs which say Mr Mohamed's treatment was "cruel, inhuman and degrading" should be released.
Mr Miliband said the ruling was "not evidence that the system is broken".
The judgement was delivered by the three most senior Court of Appeal judges in England and Wales.
The key details are contained in a seven-paragraph summary of what the CIA told British intelligence officials about Mr Mohamed's treatment in 2002. These paragraphs have now been published on the Foreign Office website.
The paragraphs concern a period in which Mr Mohamed was being held by Pakistani interrogators at the behest of the US, who suspected him of having received firearms and explosives training from al-Qaeda in Afghanistan.
They say Mr Mohamed was intentionally subjected to continuous sleep deprivation, as well as threats and inducements, including playing on his fears that he would be passed on to another country.
London learnt that the stress brought on by these deliberate tactics was increased by him being shackled during his interviews and that Mr Mohamed was eventually placed on suicide watch.
The Court of Appeal said recent events in the US courts were a key reason for releasing the UK summary of what had happened to Mr Mohamed.
Just before Christmas, a US Court ruled on a related case involving a different detainee, in which the judge provided pages of detailed information on how Mr Mohamed had been abused.
'Defend a principle'
The judge said his treatment was torture - and her reasoning was cleared for publication by the US security officials.
Following this week's ruling in London, Mr Miliband gave a statement to the House of Commons, saying he accepted the court's decision, but that the government's objection had never been about the seven paragraphs specifically.
"We have fought this case and brought the appeal to defend a principle we believe is fundamental to our national security - that intelligence shared with us will be protected by us," the foreign secretary said.
Mr Mohamed, an Ethiopian granted refugee status in Britain in 1994, was initially arrested in Pakistan in 2002 over a visa irregularity and was handed over to US officials. He was secretly flown to Morocco in 2002.
There, he says, he was tortured while interrogators asked him about his life in London - questions, he says, that could have come only from British intelligence officers.
Mr Mohamed was sent to the Guantanamo Bay detention facility, run by the US in Cuba, in 2004. He was held there until his release without charge in February 2009, when he returned to the UK.