Nur-Magomed Khatuyev stands accused of being a member of a gang led by Shamil Basayev, who has also claimed responsibility for the 2004 Beslan massacre, which took 2,000 people hostage in a hospital in the southern town of Budyonovsk in 1995.
The ensuing siege lasted for six days and eventually claimed 147 lives as the gang used civilians as human shields against a police operation.
Prosecutors in the Stavropol Territory are seeking a 14-year prison sentence for Khatuyev on charges of terrorism, banditry, and kidnapping.
Khatuyev has admitted having taken part in the raid, but his defense team has said he should be acquitted of the terrorism and banditry charges. He refused to testify during the trial.
The court was expected to convene for the verdict Monday, but the session was postponed until May 22, the press service said, without giving details.