Portugal is offering asylum for some inmates from the US detention centre at Guantanamo Bay.
In a letter to EU members this week, Portugal urged them to follow its lead.
The United States has cleared 50 to 60 detainees for release, but it cannot repatriate them due to the risk of mistreatment.
President-elect Barack Obama has pledged to close the detention centre soon after he takes office in January, but is yet to set out what will happen to the 250 men currently being held there.
In his letter on Thursday, Portuguese Foreign Minister Luis Amado said the European Union "should send a clear signal of our willingness to help the US government resolve this problem, namely by taking in the detainees".
He said "the time has come for the European Union to step forward."
A senior US official describes the offer as a "significant step".
John Bellinger, a legal adviser to the US Secretary of State, told the BBC the move was the first break in a European refusal to help shut down the camp.
The State Department said that there were 50 to 60 so-called "hard cases" at Guantanamo.
Albania is the only other country to have so far accepted detainees from Guantanamo. It took five members of China's Uighur ethnic minority on humanitarian grounds in 2006.