The government must act to ensure the last UK resident held in Guantanamo Bay is tried or released, Amnesty International has said.
Saudi-born Shaker Aamer, 43, has been held at the US detention centre for almost nine years without charge.
The human rights group urged Foreign Secretary William Hague to agree a timetable with the US for his return.
Mr Hague said he had raised the case with US Secretary of State Hillary Clinton in Washington last week.
Last week it emerged that the UK government was paying compensation to 16 men who had been detained at Guantanamo Bay. The BBC understands Mr Aamer is one of those men.
Mr Aamer had been living in the UK since 1996 when he was captured by the US after travelling to Afghanistan in August 2001.
The US claims he was fighting with the Taliban.
At the time of his capture, he was applying for British citizenship and had indefinite leave to remain in the UK. He lived in London with his British wife and three children. A fourth child has been born since his detention.
He was one of the detainees who claimed he was tortured in Afghanistan, including by US officials while British personnel were present.
Amnesty's UK director, Kate Allen, wrote to Mr Hague asking for him to make a public statement calling for Mr Aamer to either be "charged and fairly tried or released".
She also asked him to make it clear that the UK was willing to accept Mr Aamer on his release.
"When it announced financial settlements for former Guantanamo detainees last week, the government said it wanted to 'draw a line' under cases involving detention and alleged abuse overseas, yet Shaker Aamer is still languishing in a cell at Guantanamo," she said.
"Dealing with what the government calls 'legacy issues' in the 'war on terror' must mean ensuring justice for Shaker. William Hague should make it a priority that he is returned to his family in Britain."
Following his meeting with Mrs Clinton in Washington last week, Mr Hague said he "reiterated our position that we would like to see this gentleman returned to the United Kingdom and that is under consideration by the United States".
Announcing the compensation package on Tuesday, Justice Secretary Ken Clarke said it was confidential but necessary to avoid a legal battle which could have cost up to £50m.
The coalition government made it clear in the summer that it wanted to avoid a lengthy court case that also would have put the British secret intelligence services under the spotlight.
A "fully independent" investigation, chaired by former Appeal Court judge Sir Peter Gibson, is now due to look at claims that UK security services were complicit in the torture of terror suspects.