The camp is holding some 460 inmates
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Downing Street says the deaths of three inmates at the Guantanamo Bay detention camp in Cuba is a "sad incident".
Three men - two Saudis and a Yemeni - are thought to have hanged themselves with bed sheets on Saturday.
A spokesman said the US Army had promised to make an investigation, and that people should wait before making any further comment.
Briton Moazzam Begg, 37, who was held at the camp for two years, said the three suicides were "just awful".
'Unacceptable'
Prime Minister Tony Blair, a staunch ally of the US in their "war on terror", has described the camp in the Guantanamo Bay naval base as "an anomaly that has to end".
The Attorney General, Lord Goldsmith, has also described the camp as "unacceptable" and a "symbol of injustice."
The camp holds about 460 men captured in US operations around the world. There have previously been frequent but unsuccessful suicide attempts by inmates there.
Sir Menzies wants full access to inmates in the camp
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All three men had previously taken part in some of the mass on-and-off hunger strikes undertaken by detainees since last August, and all three had been force-fed by camp authorities.
They had left suicide notes, but no details have been made available.
Liberal Democrats leader Sir Menzies Campbell has said he is considering a visit to the detention camp following the suicides.
Sir Menzies told BBC One's Sunday AM the detention camp was contrary to international law.
He told the programme: "I say it is an outrage because it violates every known legal principle."
He said the idea of visiting the camp had first been proposed by the party's former leader Charles Kennedy.
Sir Menzies stressed he would only go to the camp if he was given full access to inmates.
Mr Begg, who was released from the camp in 2005, told news agency AP: "We all expected something like this but were not prepared. It's just awful. I hope the Bush administration will finally see this is wrong."
Human rights group Amnesty International is calling on the UK government to petition for the fair trial or release of eight UK citizens held in the camp.
These include Jamil el-Banna, a Jordanian refugee and long-term resident of London, and Omar Deghayes, a Libyan refugee and resident of Brighton.
The UK government so far refused to ask US authorities for the release of seven of the men on the basis that they are not UK nationals.
Amnesty International said some of the men were refugees in the UK, and could be in danger if they were returned to their home countries.