Lawyers for a British resident held at Guantánamo Bay have accused Robert Gates, the US defence secretary, of signing a "flagrantly false" affidavit to avoid having to disclose evidence of torture.

In a sworn affidavit to a district court in Washington, Gates says the US authorities have provided Binyam Mohamed's lawyers and the British government with all the information they possess relating to Mohamed's treatment while held in secret prisons. Gates declared his affidavit to be the truth "under penalty of perjury".

Clive Stafford Smith, Mohamed's lawyer and director of Reprieve, the charity that fights miscarriages of justice and human rights abuses, has told the court that Gates's affidavit is "flagrantly false". He has asked the court whether Gates was aware Mohamed was held incommunicado for three years in Pakistan, Morocco, Afghanistan and Guantánamo Bay. Stafford Smith says there seems to be only one explanation for the affidavit: the defence secretary has been "misadvised".

The claims refer to what US officials knew about Mohamed's treatment and where he was rendered to. They also refer to obligations under international law and US domestic law.

In a related development, lawyers for David Miliband, the foreign secretary, have rejected demands that documents in British hands that could prove the US was complicit in the torture should be disclosed to the media. In an unprecedented initiative, two British high court judges, Lord Justice Thomas and Mr Justice Lloyd Jones, invited the Guardian and other media to ask for the documents.

The moves are the latest in an increasingly bitter dispute over the fight to save Mohamed, 30, an Ethiopian national and British resident who faces a US military tribunal and the death penalty on unspecified terrorist charges.

Miliband's lawyers have told the high court that the media cannot see US documents that have been passed to the foreign secretary as their disclosure would cause "real damage" to national security.

They say the US has threatened to stop sharing intelligence with Britain if Miliband agrees to disclose the documents.