Democratic Unionist MEP Jim Allister issued the challenge following the emergence from hiding last Friday of three Irish republicans who have been on the run since a Colombian court found them guilty of training Marxist rebels.
Mr Allister has tabled a question in the European Parliament to be answered next month about the return of James Monaghan, Martin McCauley and Niall Connolly.
EU Governments and EU Commission officials have been asked: "Following the unimpeded return of convicted terrorist fugitives, Niall Connolly, James Monaghan and Martin
McCauley, to the Republic of Ireland from Colombia, and given the EU's declared commitment to support the fight against international terrorism, what steps has the Council of Ministers/Commission taken to ensure that the Irish Government does not provide sanctuary for these international terrorists and is the Council/Commission satisfied that Europol did everything possible to thwart their return?"
Since their arrest in Bogota in August 2001, Monaghan, McCauley and Connolly have denied claims that they were training FARC rebels.
James Monaghan repeated in a television interview on Friday their assertion that they were in Colombia to study the country's peace process.
The trio have been in hiding since the Colombian Court of Appeal overturned in December their acquittal of the charges.
Mr Allister said he had contacted every MEP to ensure they exerted maximum pressure on Taoiseach Bertie Ahern's Government to ensure it lived up to its international obligations.
"I fully intend to use the forum and facilities of the European Parliament to keep the focus on this issue, believing that it is intolerable for any civilised government to harbour terrorists," the Democratic Unionist MEP said.
The return of the men has caused problems for the Government since no extradition treaty exists between Ireland and Colombia.
Earlier yesterday, Colombian Vice-President Francisco Santos reiterated his call for Ireland to either extradite or imprison the trio.
"It is very clear, they should come to Colombia and pay the due they have with Colombian justice, which is a sentence to 17 years for training a terrorist organisation called the Farc in bomb-making, in different types of uses of explosives, which we have seen in Colombia that have become very, very dangerous and very, very damaging to Colombian civilians and Colombian military," Mr Santos said.
There were calls yesterday for a Sinn Féin member of the Northern Ireland Assembly, Caitriona Ruane, to be interviewed by police about the whereabouts of the three men.
Ulster Unionist councillor Peter Bowles urged the Police Service of Northern Ireland or gardaí to question Ms Ruane, who campaigned for the trio's acquittal in Colombia, after reports that she has been in contact with the trio since their return.
The Down UUP councillor said: "The reports at the weekend that Ms Ruane has made contact with the men were extremely disturbing but not surprising given the pivotal role Ms Ruane has played in assisting them throughout the years."