Binyam Mohamed could face the death penalty if found guilty
The government has been given a further week by the High Court to consider its refusal to disclose material involving a UK resident held in Guantanamo Bay.
Binyam Mohamed, who is facing terrorism charges, says the documents support his case that the evidence against him has been obtained through torture.
Mr Mohamed, 30, has been held at the US military prison in Cuba for four years.
On 21 August a High Court judge ruled the material should be disclosed, saying it was "essential".
The United States accuses Mr Mohamed of conspiring with al-Qaeda leaders to plan terror attacks on civilians.
He is facing a military trial in the US and could receive the death penalty if found guilty.
The US government had made a "welcome and significant" change in its position regarding documents in Mr Mohamed's case, Lord Justice Thomas said on Friday.
This had a bearing on the Foreign Office's bid to stop disclosure under public interest immunity, he said.
The British government has argued the disclosure of its material would cause "significant damage to national security of the United Kingdom".
Legal charity, Reprieve, is representing Mr Mohamed.
Its director, Clive Stafford Smith, said: "The government says it wants to help Binyam Mohamed, yet then has the nerve to pretend that the British public interest is best served by covering up America's criminal act of kidnapping and torturing him.
"It effectively says that a British resident's right to a fair trial is less important than avoiding embarrassing the Bush administration."
A Foreign Office spokesman said the court had noted the "very considerable lengths" to which the government had gone to assist Mr Mohamed.
He said: "We have never contested that Mr Mohamed's defence lawyers should have access to information which would assist him in his defence in any trial at Guantanamo Bay.
"It remains for the court to consider whether any additional benefit to Mr Mohamed from court-ordered UK disclosure outweighs the significant damage that we believe would be caused to intelligence-sharing relationships between the UK and the US, and thus to UK national security."
The decision is due in late September.