The 13 Chechens have said they will be tortured or even killed if handed over to Russia which is waging a brutal war in Chechnya to crush an independence struggle.
The court also decided to send an investigative team to Georgia and Russia to interview parties involved in the affair. The case itself will be heard later.
The men were arrested on 3-5 August, 2002 by Georgian border police at a checkpoint in the Pankisi Gorge region of northern Georgia, an area that borders Russia’s southern republic of Chechnya.
They were held on charges of illegally crossing the border and unlawfully possessing and trading firearms.
Moscow has demanded their immediate extradition, claiming the men are terrorists who fought in the conflict between the state and the Caucasus republic.
Georgian authorities handed five of the men over to Russia on 4 October 2002, but have suspended further extraditions until the outcome of the case.