Amnesty International urged the US to "end the lawlessness" of its facility, which is holding about 460 people.
"The news that three detainees in Guantanamo have died as a result of apparent suicide is a further tragic reminder that the US must end the lawlessness of the facility," it said in a statement.
Anders Fogh Rasmussen, the Danish prime minister, said on Saturday that the detention of the men went against basic rule of law.
"I think it would be to the benefit of our cause and our fight for freedom and against terrorism if the facilities at Guantanamo were closed down," he told CNN television channel.
Harriet Harman, a senior British minister, also questioned the facility's legitimacy.
"If it is perfectly legal and there is nothing going wrong there, why don't they have it in America?" she told the BBC.
The men, two Saudis and one Yemeni national, used nooses made of sheets and clothes to hang themselves.
Attempts by prison guards and medical teams to resuscitate the men were unsuccessful, a US spokesman at Guantanamo Bay said.
"They have no regard to life, neither ours nor their own"
Rear Admiral Harry Harris, Guantanamo camp commander
They were the first reported deaths among detainees held at the isolated base. Of those held at Guantanamo, only 10 have been charged with any crime, and none has gone to trial.
Rear Admiral Harry Harris, the camp's commander, described the suicides as an act of warfare.
"They are smart, they are creative, they are committed," he said of the prisoners.
"They have no regard to life, neither ours nor their own... I believe this was not an act of desperation, rather an act of asymmetric warfare waged against us."
However, Shafiq Rasul, a British former Guantanamo prisoner released in March 2004, told Sky News that he had witnessed suicide attempts by prisoners who had "just had enough".
"There were individuals who had just had enough, [who] couldn't take any more and were going crazy, who would attempt to kill themselves," he said on Sunday.
"There were individuals who had just had enough, [who] couldn't take any more and were going crazy, who would attempt to kill themselves"
Shafiq Rasul, former Guantanamo inmate
There have been 41 suicide attempts by 25 detainees since the US began transferring suspects to the camp in January 2002.
Most were captured during the US-led war against the former Taleban government in Afghanistan in late 2001.