The State alleges the man is the “foremost organiser and facilitator of travel by extremists prepared to undertake violent action” on behalf of Islamic State (IS) and its “main recruiter” in Ireland.
The man, who cannot be identified, denies claims he has consulted with senior violent extremist leaders outside Ireland, represents a threat to national security, or recruits members for Islamic extremist groups.
He claims he was tortured in Jordan during the 1990s due to his political activities, and fears torture if returned.
At a late sitting of the High Court on Monday, Mr Justice Richard Humphreys, who last month dismissed the man’s actions aimed at preventing his deportation, refused to allow him bring an appeal.
The judge also refused the man’s application to have the case referred to the Strasbourg-based European Court of Human Rights.
The man sought permission to bring an appeal against the judge’s decision, arguing the case raised points of law of exceptional importance that need to be determined by the court of appeal.
The justice minister opposed the application, arguing that no point of law of exceptional importance had been raised.
The judge, who said he would give detailed reasons for his decision at a later date, agreed with the minister that no point of law of exceptional public importance had been raised.
The man also sought a stay on any deportation order to allow his lawyers apply to the Supreme Court and the European Court of Human Rights.
The judge also refused that application and said the case had been before a number of courts, including the European Court of Human Rights and had been determined by the High Court.
While the court’s decision clears the way for the minister to deport the man, it is believed his lawyers will continue to pursue the matter in a bid to prevent his deportation.
The man was not in court for the ruling. He has lived here since 2000, on the basis of having an Irish citizen child. Last year, the authorities decided not to renew his residency permit because the child had not been residing in the State and was living with his mother elsewhere.
In his judgement last month, Mr Justice Humphreys said this was not a case where a person who had previously been tortured was being deported to face further torture. Rather, it was a case where the man had failed to persuade the minister “either of the veracity of his account of previous ill treatment or of a real risk of future ill-treatment”.