The U.N. human rights agency said that the suicides could have been anticipated and the focus now should be on closing the facility. The European Parliament renewed its calls for closure.
The highest priority in the wake of the deaths of two Saudi men and one Yemeni Saturday is working out how to close the camp and what to do with the detainees, said Jose Diaz, spokesman for the U.N. High Commissioner for Human Rights.
"It's not completely unexpected that this should happen," Diaz said. "The focus of attention should be on closing Guantanamo."
EU lawmakers urged the United States to stop subjecting prisoners to what they called arbitrary detention in violation of international legal and human rights standards, and to stop using interrogation techniques such as dunking detainees in water, shackling them to the floor to limit movement, and sexually humiliating them.
In a resolution, the legislators gave the United States credit for making progress in improving conditions for the detainees, "in particular with regard to medical care, nutrition, the expression and exercise of their religious rights and recreation."
But the resolution also said the Guantanamo prisoners still are detained without a fair hearing by an impartial tribunal.
The EU has become increasingly vocal in urging Washington to close the prison camp in southeast Cuba where about 460 people are being held on suspicion of links to al-Qaida and the Taliban. The EU is expected to raise the issue at an EU-U.S. summit in Vienna next week.
Separately, the U.N. special investigator for torture said in Germany that Guantanamo should be closed this year.
A good opportunity for announcing the closure would be President Bush visit to Austria for the EU-U.S. summit June 21, Manfred Nowak told German radio station Deutschlandradio Kultur.
"I think that it will certainly be closed this year," he said. "But I could imagine that the recent suicides in Guantanamo Bay could speed up this decision's process."
Bush has defended the detentions, while saying his ultimate goal is to see Guantanamo emptied through releases or transfers of prisoners to their home countries.