The three detainees were the first reported deaths among hundreds of detainees held at the isolated base. Some have been held for as long as four and a half years without charge.
Two men from Saudi Arabia and one from Yemen were found "unresponsive and not breathing in their cells" early on Saturday, according to a statement from the Miami-based US Southern Command, which has jurisdiction over the prison.
Saudi Arabia has begun procedures to receive the bodies of the two Saudis, whom it identified as Mani bin Shaman bin Turki al Habradi and Yasser Talal Abdullah Yahya al Zahrani, Interior Ministry spokesman Mansour Turki told the Associated Press on Sunday.
The identity of the Yemeni was still not known.
The US military's Joint Task Force at Guantanamo said that "the three detainees were pronounced dead by a physician after all lifesaving measures had been exhausted".
"They hanged themselves with fabricated nooses made out of clothes and bedsheets," Navy Rear Admiral Harry Harris said.
Military officials said the suicides were co-ordinated and Harris described them as an act of war.
The suicides come amid growing
defiance at the prison
"They have no regard for human life," he said.
"Neither ours nor their own. I believe this was not an act of desperation but an act of asymmetric warfare against us."
One of the detainees was a mid- or high-level al-Qaida operative, while another had been captured in Afghanistan and participated in a riot at a prison there, Harris said. The third belonged to a splinter group, he added.
All three men left suicide notes but US military officials would not describe what they said.
In a statement to the al-Riyadh newspaper on Sunday, the state-sponsored Saudi Human Rights group blamed the US for the deaths and suggested torture was the real cause of death - or that it pushed the men to suicide.
Mufleh al-Qahtani, the group's deputy director, said: "There are no independent monitors at the detention camp so it is easy to pin the crime on the prisoners, considering its possible they were tortured."
"There are no independent monitors at the detention camp so it is easy to pin the crime on the prisoners, considering its possible they were tortured"
director, Saudi Human Rights group
He said his organisation will carry out its own investigation into the cause of the two deaths.
Tony Snow, the White House spokesman, said George Bush, the president, "expressed serious concern" when told of the deaths.
Guantanamo officials say there have been 41 suicide attempts by 25 detainees, but no deaths since the US began taking prisoners to the base in January 2002.
Defence lawyers contend that the number of suicide attempts is higher.
To help prevent more suicides, guards will now give sheets to detainees only when they go to bed and remove them after they wake up in the morning, the base commander said.
About 460 men - suspected of links to al-Qaeda or the Taliban - are being held at Guantanamo but only 10 have been charged with crimes and face military tribunals.
The Supreme Court is expected to rule this month on whether Bush overstepped his authority by ordering the tribunals.
Pushed to death
Moazzam Begg, 37, a British Muslim who spent three years in US detention, including two years at Guantanamo, before being released in 2005, told The Associated Press: "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."
Barbara Olshansky of the Centre for Constitutional Rights, which represents about 300 Guantanamo Bay detainees, said it was not surprising that the three men committed suicide.
Moazzam Begg, an ex-detainee,
says suicides were expected
"I think people [detained at Guantanamo] have this incredible level of despair that they will never get justice.
"And now they are gone. And they died without ever having seen a court."
Olshansky said the US government "not only failed these people but pushed them on the road to death".
The suicides come amid growing defiance at the prison.
On May 18, a detainee staged a suicide attempt to lure guards into a cellblock where they were attacked by prisoners armed with makeshift weapons, the military said.
"I think people [detained at Guantanamo] have this incredible level of despair that they will never get justice ... [the US] not only failed these people but pushed them on the road to death"
Centre for Constitutional Rights
Earlier that day, two detainees overdosed on antidepressants they collected from other detainees and hoarded in their cells.
The men have since recovered.
There also has been a hunger strike among detainees since August. The number of inmates refusing food dropped to 18 by last weekend from a high of 131.