The European Parliament has voted overwhelmingly in favour of a motion calling on the US to close the Guantanamo Bay detention camp.
The suicides were the first at the base, despite dozens of attempts
It follows the suicides of three detainees over the weekend.
Austria, which holds the EU presidency, said it would urge US President George Bush to close the camp when EU leaders meet him at a summit next week.
Austrian Foreign Minister Ursula Plassnik said the US base in Cuba was "an anomaly".
"The government of the United States should take measures to close Guantanamo as quickly as possible," Ms Plassnik said.
The European motion carries no legal weight but it is an indication of the level of concern in the EU about Guantanamo, reports the BBC's Alix Kroeger in Strasbourg.
The UN human rights agency has also repeated calls for the camp to close, saying the deaths were "not completely unexpected".
"The focus of attention should be on closing Guantanamo," said Jose Diaz, spokesman for the UN High Commissioner for Human Rights.
The International Committee of the Red Cross (ICRC) has said it plans to make a special visit to Guantanamo in the coming days.
A spokesman told the BBC the purpose of the visit was to assess what happened from the detainees' perspective and to check the overall mood in the camp. It will not be an inquiry into the deaths.
The three men who died - two Saudis and a Yemeni - had been visited by the ICRC, which sends delegates to Guantanamo every six to eight weeks.
However, news of the suicides prompted the Red Cross to tell Washington it wanted to visit the base as soon as possible.
Concerns have been raised over the mental health of the detainees, some of whom have been held for four years.
A former Muslim chaplain at Guantanamo said conditions at the camp were driving inmates to suicide.
"It was bound to happen. The conditions down in Guantanamo were quickly deteriorating way back in 2002 and 2003 when I was assigned there," James Yee told the BBC's World Today.
"And these prisoners are now well into their fifth year of detention - indefinite detentions, lack of due process, no charges.
"That all has to do with contributing to these suicides, in my opinion."
The US response to the suicides has come under international criticism.
Base commander Rear Adm Harry Harris described them as an "act of asymmetric warfare waged against us", while deputy Assistant Secretary of State for Public Diplomacy Colleen Graffy told the BBC the deaths were "a good PR move".
She described them as "a tactic to further the jihadi cause".
However, the US state department has sought to distance itself from those comments.
"I would not say that it was a PR stunt," said spokesman Sean McCormack.
There have been dozens of unsuccessful suicide attempts at Guantanamo Bay, which holds some 460 prisoners.