The US has 50 to 60 detainees whom it has been unable to repatriate
The European Parliament has urged EU member states to help the US shut down the Guantanamo Bay prison camp by accepting some detainees.
A resolution on Guantanamo was passed by a large majority of MEPs - 542 for, 55 against and 51 abstentions.
It called for EU states to accept low-risk prisoners who cannot be sent home for fear they might be mistreated.
"Europe cannot stand back and shrug its shoulders," said the Liberal bloc's leader, Graham Watson, during a debate.
US President Barack Obama has signed an order to shut Guantanamo within a year.
Last week, EU foreign ministers said they wanted to help on humanitarian grounds, but could not act until the US demonstrated the prisoners did not pose a credible security risk.
Albania is the only country to have so far accepted Guantanamo detainees on humanitarian grounds, taking in five members of China's Uighur ethnic minority in 2006.
MEPs discussed the closure of Guantanamo and the fate of its detainees in a parliamentary debate in Strasbourg on Tuesday, before Wednesday's vote.
Graham Watson MEP said the EU must not "stand back and shrug its shoulders and say these things are for America alone to sort out".
One of the lessons to be learned from the era of former US President George W Bush was that "in the administration of international justice, the go-it-alone mentality ends in a cul-de-sac of failure", he said.
"Too often member states from our union were complicit in what the Bush administration did," he added, apparently referring to allegations that member states helped the CIA carry out extraordinary renditions of terrorism suspects.
However, conservatives in the EPP-ED coalition warned that resettling detainees could entail risks for Europeans and that security concerns had to be given priority.
"Many past and present detainees were trained in terror camps in Afghanistan," said EPP-ED vice-chairman Hartmut Nassauer. "These people are potential terrorists and we have a duty to protect Europe's citizens."
The US has said there are 50 to 60 so-called "hard cases" at Guantanamo, including several Chinese Uighurs, whom it has been unable to repatriate because of concerns over what might happen to them if they were repatriated. Libyan, Uzbek and Algerian detainees are also said to be at risk.
Clive Stafford Smith of the legal charity Reprieve, which has represented many of the detainees, argues that having criticised Guantanamo for so long, Europe now needs to be part of the solution.
"You know when America held people in Guantanamo and said they had no legal rights, we as European said they were humans and had human rights," he told the BBC.
"It would be sort of hypocritical for us now in Europe to say these are American problems, not human problems, and refuse to reciprocate in trying to solve what is a problem for everyone."
The BBC's Dominic Hughes in Strasbourg says there is also the pressing issue of the rehabilitation of men who have spent up to seven years in a high-security prison.
A task force in the US has 30 days to recommend where the 245 remaining detainees should go - so far no formal request has been made of the EU.
Countries like Portugal and the UK want to send a positive message to the Obama administration, our correspondent says.
Others like the Netherlands are more reluctant - arguing an American problem needs an American solution, he adds.