"Russian troops are currently disarming the surrounded Georgian forces in South Ossetia," Col. Gen. Anatoly Nagovitsyn, deputy head of the General Staff, told a news conference.
Russian troops are currently forcing all Georgian troops out of Georgian-populated villages in the east and west of the breakaway region, he said.
Russian President Dmitry Medvedev said earlier on Monday that the operation declared on Saturday to "force Georgia to accept peace" was almost complete.
Russia drove Georgian troops out of the devastated capital of South Ossetia, Tskhinvali, on Sunday, two days after Tbilisi launched a major ground and air offensive to regain control of the pro-Russian region.
Shelling and bombing attacks continued on Monday morning. Russia, which has maintained peacekeepers in the region since conflicts in the early 1990s, said over 2,000 civilians have been killed by Georgian forces. Moscow has also highlighted a humanitarian catastrophe in the region.
Georgia says it has lost 150 people in the conflict, and that hundreds of Georgians are injured. Nagovitsyn said 18 Russian troops have been killed and 52 wounded.
He warned that in the Black Sea near Georgia's other breakaway region, Abkhazia, Russian forces will attack all Georgian ships and aircraft entering the security zone to deter a Georgian attack on Abkhazia.
Earlier reports said Russia had sent more than 9,000 troops and 350 armored vehicles into Abkhazia.
On Saturday Russia sent vessels to patrol the area near Abkhazia, where martial law has been declared. On Sunday, Russian defense officials said one Georgian missile boat was destroyed after it attacked Russian ships.
Nagoviotsyn also said two more Russian military aircraft have been downed in the conflict zone in the past 24 hours, bringing the Air Force's overall losses to four aircraft. He said Russia has gained full control over Georgian airspace, and is preventing all flights by Georgian combat aircraft.
"We have eliminated the possibility of an aerial threat from Georgia in the Georgian-South Ossetian conflict zone," Nogovitsyn said.
He denied Georgian claims that Russian warplanes have targeted Georgian oil pipelines in bombing raids, in particular the Baku-Tbilisi-Ceyhan, which pumps crude from the Caspian to Europe.
"We did not bomb Georgia's oil pipelines. If we had done this, oil spills and possible oil fires could have led to a regional environmental disaster," Nogovitsyn said.
The general also denied reports that Russia had dropped bombs on Tbilisi's international airport or any other civilian targets, but admitted to an attack on a radar facility.
The United States and other Western nations have criticized Russia for what they have called a 'disproportionate' response to Georgia's attack on South Ossetia, and are urging both Russia and Georgia to stop armed hostilities.
Georgian President Mikheil Saakashvili, who seeks NATO membership for the South Caucasus country, has pledged to bring the two pro-Russian separatists republics under central control. Most people in both republics have Russian passports.
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News that Moscow Mayor Sergei Sobyanin would resign in order to run for the mayoral election in September came as quite a shock. Sobyanin’s political potential is fairly dubious, not to mention his approval ratings. He has not finished many of the projects he initiated and the electoral effect from these projects is expected to come a bit later than September 2013. Sobyanin’s opponents were not entirely unprepared for this blitzkrieg.