Georgian police arrested Marina and Alexander Goncharov on April 23 after they crossed the border between Abkhazia and Georgia near Psou without entry visas.
Defense lawyer Vissarion Rigvava said the defense acknowledged the couple had no entry visas, but "there are no grounds to claim that the defendants had some anti-state motives."
A representative of the Russian Orthodox Church in Georgia testified in the court that the couple was traveling to the Black Sea port of Poti to visit a relative's grave and offered to stand bail, but the court rejected the arguments presented by the defense and the testimony of the church official.
The court will announce its final decision in two months after the investigation is completed.
The Goncharovs face up to five years in prison if convicted.