A cross-party coalition of MPs and human-rights campaigners has written to Barack Obama calling on him to publish secret documents that allegedly contain evidence of US and British complicity in torture.

The move came as David Miliband, the foreign secretary, defended his position on the Guardian website over the suppression of evidence of the torture of Binyam Mohamed, the former UK resident held in Guantánamo Bay.

"Far from suppressing evidence, it was our efforts that got documents disclosed to Mr Mohamed's lawyers," Miliband wrote. He was referring to the handing over of 42 US intelligence documents to Mohamed's lawyers for the purposes of a secret military trial in the US.

The lawyers have had to sign an order that they would not disclose the contents of the documents. The high court in London has made it clear that it believes that what it calls the "powerful evidence" ought to be disclosed. The judges said they could not order the disclosure because, according to Miliband, the US said it was likely to cause "real damage" to British and American national security and harm intelligence-sharing between the two countries.

Miliband told MPs it was not his job to lobby Washington on the issue. It later emerged that it was his officials who had proposed to the US state department that it write a letter to the high court objecting to disclosure.

In today's article, Miliband says he would have "no objection" to the US deciding to publish the documents.

The letter to Obama calling on the president to publish them has been signed by Edward Davey, the Liberal Democrats' foreign affairs spokesman, Andrew Tyrie, the chairman of the all-party parliamentary group on extraordinary rendition, Chris Mullin, a former Foreign Office minister, Clare Algar, the executive director of the legal charity Reprieve, and Kate Allen, the director of Amnesty International UK.

Davey said today: "With the foreign secretary refusing to lobby the US to release these documents, I felt others had to do his job for him. It is a total dereliction of duty for the foreign secretary not to push this case with the Obama administration, given this involves something so serious as torture."

He added: "So it is important that a direct request to President Obama comes from British MPs and civil society. The government's claims to oppose torture sound hollow when it fails to pursue the publication of evidence that may uncover it."