Espionage charges have been officially filed against the four men who were detained on Wednesday, said Shota Khizanishvili, spokesman for the interior minister.
Russia has recalled its ambassador from Tbilisi and started evacuating some officials after Georgia announced the arrests of four GRU (Russian army intelligence) officers and more than 10 Georgian citizens.
Sergei Lavrov, the Russian foreign minister, said in televised comments: "We have demanded the immediate release of our citizens and we will achieve this with all the means available to us."
A Russian cargo plane landed in Tbilisi on Friday to pick up some of the several hundred Russian officials based in the southern Caucasus country, and take them home.
Vyacheslav Kovalenko, the Russian ambassador told journalists that: "At least more than 100 people will leave today."
He added that a second plane was scheduled to arrive from Moscow.
Mikhail Saakashvili, the Georgian president, has dismissed Moscow's reaction as "hysteria".
"Georgia is acting just as any other democratic state would do, for instance Britain, Poland, the United States or any other country," he said.
Saakashvili has described the
Russian response as 'hysteria'
In New York, Russia urged the UN security council to put pressure on Tbilisi to withdraw its troops from part of the Abkhazia region that has declared itself independent of Georgia.
A Russian draft statement circulated among the council's 15 members would appeal to all sides to refrain from any action that threatened the UN-backed peace process between Georgia and Abkhazia and urge Tbilisi to reconsider plans to declare a new republic there.
Moscow supports the breakaway province by paying pensions, issuing Russian passports to its residents, allowing cross-border traffic and stationing Russia troops there.
Georgia accuses Russia of backing Abkhaz separatists.
Relations between Moscow and Tbilisi have become increasingly tense since Saakashvili came to power after the 2003 "Rose Revolution," pledging to reduce Russia's influence in the country.
Moscow dislikes Saakashvili's pro-Western policies, including joining Nato, and his public attacks on Russia.
Russia has two military bases in Georgia - relics of Soviet-rule - which it is due to leave in 2008.