Irish Prime Minister Bertie Ahern has said the return of three republicans sentenced in Colombia created "enormous difficulties" for the peace process.
The three Irishmen each received 17 year sentences
Niall Connolly, Martin McCauley and James Monaghan were sentenced to 17 years in jail for training rebels but vanished in December while on bail.
They returned to the Irish Republic and Colombia wants them to be extradited.
Mr Ahern said it would be a matter for the courts alone and that no deal had been done over the men with Sinn Fein.
Speaking in County Kerry he said the men's situation was never part of political discussions with Sinn Fein, and there had been no deal done for their return.
BBC News' John Thorne said Mr Ahern had described suggestions that a deal had been done as "false, untrue and unhelpful".
Colombia's vice-president said Irish authorities had a "legal and moral obligation" to return the republicans.
Currently, the two countries do not have an extradition treaty.
Colombian Vice-President Francisco Santos said in a statement: "Irish Prime Minister Bertie Ahern must demonstrate his country's commitment to the global fight against terrorism."
The Colombian police are believed to be preparing an extradition warrant for the trio.
Unionists greeted the men's return to the Irish Republic with anger, but it was welcomed by Sinn Fein.
Irish state broadcaster RTE reported the trio had returned in recent days.
Jim Monaghan, interviewed by RTE at a secret location, denied that any deal had been done with the British or Irish governments following the IRA's statement last week in which it said it was ending its campaign of violence.
He said he did not consider himself to be "on the run" and would not be hiding from Irish police.
Monaghan would not say how the three men got back to the Republic of Ireland, but that they had got "a lot of help from a lot of people" and that he would not endanger them.
He said he hoped the Irish government would not place any obstacles in the way of the three men staying in the country, adding it would be "very remiss to send anyone back to Colombia".
He said the men would be seeking legal advice about the possibility of extradition back to Colombia.
Intelligence sources believe the three Irishmen left via Venezuela before going to Cuba, where Niall Connolly had been Sinn Fein's representative, BBC correspondent Jeremy McDermott reported from Colombia.
Mr Santos said: "They have a judicial sentence over their heads and we sincerely hope that they pay jail for it.
"We hope that the international police system will hand them over to Colombia, even though that's difficult because there's no extradition treaty between Ireland and Colombia."
Irish deputy prime minister Mary Harney said there were "very serious issues to be addressed, seeing as they were travelling on false passports".
And a Northern Ireland Office spokesman said: "We have only just become aware of the presence of these men in the Republic of Ireland.
"That is a matter for the Irish authorities. If they enter the UK, an extradition request will be dealt with without delay."
The men, who had been accused of being IRA members, were arrested in Bogota in August 2001.
They were found guilty of travelling on false passports, in June 2004, but were acquitted of training Revolutionary Armed Forces of Colombia (Farc) guerrillas.
Farc has waged a 40-year insurgency in Colombia
That decision was reversed after an appeal by the Colombian attorney general and they were sentenced to 17-year terms.
A judge had ordered the men to remain in the country pending the outcome of the appeal.
An international arrest warrant was issued for them after they disappeared.
McCauley, 41, is from Lurgan in County Armagh, Monaghan, 58, is from County Donegal and Connolly, 38, is from Dublin.