The Foreign Ministry also announced a partial evacuation of Russian personnel and their families from Georgia because of a "growing threat to their security."
The evacuation will start on September 29 and will be conducted by aircraft of the Emergency Situations Ministry.
The Foreign Ministry also advises Russians to refrain from trips to Georgia.
Earlier in the day, Russia's Defense Minister Sergei Ivanov described the detention of the four Russian officers as "outrageous."
MORE: Coverage of this topic in Russian from RFE/RL's Russian Service.
"All [recent] actions by Georgian authorities can be characterized as utterly outrageous, as an open desire to provoke the Russian Federation, with the type of hysteria typical of the Georgian authorities, into acting inadequately," Ivanov said. "Naturally, we demand resolutely the immediate release of all the [detained] Russian officers. Russia's reaction to these events will be adequate and sensible."
According to Georgian Interior Minister Vano Merabishvili, the four were members of the Russian military intelligence service. He said they were detained along with more than 10 other people in the Georgian capital, Tbilisi, and the Black Sea port of Batumi, on charges of espionage.
Russian Foreign Minister Sergei Lavrov today called their detention part of Georgia's "anti-Russian policy" and urged the United Nations Security Council to step in to resolve the matter.
Lavrov spoke to reporters today in Russia's Far East, as Georgian police were surrounding the Tbilisi headquarters of Russian forces in the South Caucasus.
Russia Demands Return Of Detainees
"This can only be regarded as yet another manifestation of an anti-Russian policy," Lavrov said. "We have demanded that our citizens be handed over immediately. We will stand firm in securing their release by all means available to us."
Lavrov also criticized Georgia's increasingly close ties to NATO and said the crisis merited the attention of the UN Security Council.
Speaking to reporters today in Moscow, Ivanov accused Georgia of violating agreements on the withdrawal of Russian forces from Georgia, where Moscow has retained two former Soviet military bases.
"All of this is being done [by Georgia] to force out our peacemakers by all possible means, to make their status illegal, while violating absolutely all agreements that have been achieved earlier on peacekeepers and on the procedure of withdrawing the Russian military bases from Georgia," Ivanov said.
Russian news agency reports say that Ivanov also warned that Russia would deliver an "appropriate" response to Georgia and compared the arrests of the Russian officers to 1930s repression by the regime of Georgian-born Soviet dictator Josef Stalin.
Detainees Accused Of Spying
On September 27, Georgian Interior Minister Merabishvili said the four members of the Russian military intelligence service were detained along with more than 10 others people in the Georgian capital, Tbilisi, and the Black Sea port of Batumi.
"The main objects of their interest were the defense of Georgia, problems of integration with NATO and future plans, the energy security of Georgia, opposition political parties and NGOs, certain units of the Defense Ministry, personnel as well as arms, military purchases, seaports, railway communications and transport capacity, and the military units deployed in the conflict zones," Merabishvili said.
Russian Defense Minister Ivanov also claimed today that six Russian servicemen had been detained and beaten by Georgian police near the western Georgian port of Batumi before being released.
However, no other Russian officials spoke of this and Georgian officials could not immediately confirm the assertion.
After being summoned to Russia's Foreign Ministry, Georgian Ambassador to Moscow Irakli Chubinishvili said today that Russia was protesting the move and is asking for the immediate release of the four officers.
News agencies also reported today that the Russian Embassy in Tbilisi has suspended the issuance of visas to Georgian citizens for travel to Russia.