Russia has been criticised for withdrawing its troops too slowly after signing a peace agreement with Georgia, but on Thursday pledged to have its forces within a buffer zone by Friday.
An emergency session of Russia's upper house of parliament on the issue of the breakaway provinces is set for Monday.
Russian tanks poured into Georgia on August 8 to repel an attempt by Georgia's United States-trained army to seize control of South Ossetia.
The troops drove Georgian forces from their foothold in Abkhazia, occupied several strategic towns and roads, and destroyed Georgian military facilities in the strategic Caucasus nation.
Anatoly Nogovitsyn, the deputy chief of the Russian military's general staff, said: "The pullback has started at such a pace that by the end of August 22 all the forces of the Russian Federation will be behind the line of our zone of responsibility."
On Thursday, the news agency Reuters reported seeing a column of Russian tanks, armoured personnel carriers and artillery moving across the border into Russia.
"I can see 21 T-72 tanks moving towards the Roki tunnel in the direction of Russia," said the reporter. The tunnel is several kilometres from the Georgian-Russian border and is the main access route for Russian forces.
"I can also see four Grad artillery launchers, several armoured personnel carriers and heavy trucks ready to move into the tunnel."
Meanwhile, aid workers from the International Committee of the Red Cross (ICRC) arrived at the main hospital in Tskhinvali, the capital of South Ossetia, to assess needs there.
The ICRC team arrived late on Wednesday after trying for a week to reach the province, which is under Russian military control.
"Now the hard work starts, evaluating the needs and dealing with protection issues," Anna Nelson, a spokeswoman in Geneva, said.
"They are visiting the main hospital which was damaged and evaluating the state of facilities."
Russia says 1,600 people, mainly civilians, were killed when Georgian forces tried to retake the pro-Moscow province, which broke away from Georgia in the 1990s.
The figure has not been independently verified.
|Many South Ossetians are missing family members [AFP]
Jakob Kellenberger, the ICRC president, sought access to South Ossetia for the humanitarian agency in his talks with Sergei Lavrov, the Russian foreign minister in Moscow, on Tuesday.
The ICRC convoy reached South Ossetia via Vladikavkaz in North Ossetia, part of the Russian Federation.
During the seven-hour drive, they saw burnt-out cars and "got an overall feeling of desolation," Nelson said.
Residents immediately approached the ICRC team for help in locating missing family members, she said.
"Some knew their family had gotten out and reached safe shelter and wanted to re-establish contact, others were saying they didn't know what happened to their loved ones."
The ICRC is also holding talks with South Ossetian authorities to gain access to people detained or arrested in connection with the conflict.
"Overnight they heard isolated shooting as well as explosions which, it seems, were part of demining efforts. It has got residents on edge," Nelson said.
"Store shelves appear to be empty. But they got the impression that the Russian government was very present and providing assistance and meeting basic needs."
The team is also explaining to civilians the danger of unexploded munitions left over from the fighting.