A High Court judgment on the extradition of Ian Bailey, which had been expected today, will not be delivered until later this year.
The 53-year-old from Cork is wanted by French authorities in connection with the death of French filmmaker Sophie Toscan Du Plantier 14 years ago.
Mr Justice Michael Peart has invited further submissions on the case in light of a recent Supreme Court decision in another extradition case.
Lawyers for Mr Bailey said that decision indicates it is not permissible to surrender someone to another jurisdiction for the purposes of an investigation.
Mr Bailey of the Prairie, Schull in west Cork, was arrested during the investigation into Ms Du Plantier's death in the 1990s, but no charges were brought against him.
He has always denied any involvement in killing of the 39-year-old French woman whose body was discovered near her holiday home on 23 December 1996.
His lawyers said attempts by French authorities to have him extradited were an insult to the Irish State.
They came as a complete shock to Mr Bailey in 2009 while he was preparing for his law exams, they said.
They also argued that until 2005 he could not have been extradited for a crime with which the Director of Public Prosecutions had decided not to charge him.
However, the law changed in 2005 but Mr Bailey's lawyers argued that under Irish law there would now have to be new evidence to prosecute him.
The case will return to the High Court on 10 February for submissions.
