The High Court has refused to carry out a review of the DPP's decision not to prosecute Algerian-born Irish citizen Ali Charaf Damache on terrorism charges.
The 48-year-old is facing extradition to the United States where he is accused of conspiring with others to create a violent jihad organisation in Europe capable of targeting both US and European citizens.
Ali Charaf Damache is alleged to have conspired online with American woman Colleen LaRose and others to create a terror cell in Europe.
LaRose, who called herself Jihad Jane, was recently jailed in the US for her role in a plot to shoot a Swedish cartoonist for depicting the Muslim prophet Mohammad on the head of a dog.
Damache, also known as the Black Flag, is fighting his extradition to the United States to face terrorism charges that could see him jailed for up to 45 years.
His lawyers want to know why he was not prosecuted by the DPP for offences that are alleged to have occurred while he was living in Ireland.
They claim the Irish state has unlawfully delegated the prosecution to the US without any explanation.
However the High Court has refused to review the director's decision. Mr Justice John Edwards will explain why in a 100-page written judgment this Friday.