Six Russian soldiers and officers have been detained over the last 24 hours for allegedly being involved in espionage.
"The files reliably show officers of Russia's Main Intelligence Directorate personally conducting intelligence activities, personally recruiting Georgian nationals and carrying out unlawful activities," Vano Merabishvili told a briefing.
The minister also said that during the arrest, Georgia had taken into account all international norms. Charges will be brought Friday.
Tensions between Russia and Georgia have been rising in the past few years over the presence of Russian peacekeepers in the breakaway Georgian republics of Abkhazia and South Ossetia, and the current scandal has done nothing to improve the atmosphere.
The Russian Foreign Ministry said Wednesday that the accusations were "unsubstantiated" and called them "the latest gross attack that confirms that anti-Russian course of the Georgian leadership."
Sergei Ivanov, Russia's defense minister and also a deputy prime minister, also raised the temperature Thursday by saying seven other Russian servicemen - a junior officer and six soldiers - had been subjected to violence when their car was stopped in the western city of Batumi on Wednesday night.
"They were beaten up, [and] their weapons and car were confiscated," he said. "Then at about 3 a.m. (11 p.m. GMT) they were released."
Ivanov described the Georgian authorities' actions as "total lawlessness and hysteria."
But Shota Khizanishvili, a spokesman for the Georgian Interior Ministry, categorically denied the assault accusations. "That did not happen," he said. "Police did not beat up the Russian servicemen."