"A significant part of the operation to force the Georgian authorities to make peace in South Ossetia has been concluded," Medvedev said. "Tskhinvali is under the control of a reinforced Russian peacekeeping contingent."
Oil prices were volatile on Monday.
French President Nicolas Sarkozy prepared to fly to Georgia and Russia on Tuesday on a peace mission, following a round of shuttle diplomacy by his foreign minister.
As fighting continued in the Caucasus crisis which has alarmed Western governments and shaken world oil markets, U.S. President George W. Bush accused Russia of a "disproportionate response" and the European Union demanded Moscow halt military activity in Georgia.
The Kremlin rejected a Georgian ceasefire proposal made on Sunday, saying its information on the ground indicated Tbilisi was continuing to fight. "Georgia continues to use force and in this regard we cannot consider this document," a spokesman said.
The simmering conflict between Russia and its small, former Soviet neighbour erupted last Thursday when Georgia suddenly sent forces to retake South Ossetia, a pro-Russian province that threw off Georgian rule in the 1990s.
Moscow responded with a counter-attack by its vastly bigger forces that drove Georgian troops out of the devastated South Ossetian capital Tskhinvali on Sunday. Russia says more than 2,000 people have been killed in the fighting and thousands more are homeless but these figures are not independently verifiable.
Women and children wept in the streets of Tskhinvali on Monday as they surveyed the destruction amid continued Georgian shelling. Russian troops distributed water and food from trucks.
One elderly resident told Reuters how she sheltered in a cellar with her 7 year old grandson during the bombardment. "My grandson screamed: 'Uncle Putin please help us, help us so that the Georgians don't kill me !'. They were screaming and crying it was terrible, a nightmare," she said. "Thank God the Russians have come. It is getting better."
Russia and Georgia engaged in a bitter war of words on Monday about their conflict, with numerous claims and counter-claims and few independently verifiable facts.
Saakashvili told reporters that Russia "wants to replace the government in Tbilisi" and claimed Moscow wanted to seize control of energy routes in the region.
Georgia also claimed Russian tanks had advanced beyond South Ossetia towards the Georgian town of Gori -- Stalin's birthplace -- and that Russia had attempted to bomb a key oil pipeline, allegations not so far substantiated by independent witnesses.
Moscow insisted it had not moved its troops beyond the territory of South Ossetia and a second separatist region, Abkhazia, and said it would not push further into Georgia.
President Dmitry Medvedev said the operation to restore calm in South Ossetia was nearing its conclusion -- a comment which led to a brief recovery rally among battered Russian stocks.
The Russian General Staff said at a military briefing that staying within South Ossetian borders was a "key principle".
Prime Minister Vladimir Putin, who has taken a leading role in the crisis, attacked the United States for helping Georgia fly home troops from Iraq and said the West was mistaking the aggressors for victims in the conflict -- a reference to strong Western support for Georgia and criticism of Moscow.
"The very scale of this cynicism is astonishing," Putin said in televised remarks to a government meeting. "The attempt to turn white into black, black into white and to adeptly portray victims of aggression as aggressors and place the responsibility for the consequences of the aggression on the victims."
Despite international calls for peace, both sides continued to fight on Monday. Georgia shelled Tskhinvali early in the day despite declaring a ceasefire on Sunday, and Tbilisi said Russian jets had bombed Georgian targets again overnight.
Russia said at a daily military briefing that it had lost four military aircraft and 18 soldiers since the fighting started, with another 14 missing in action and 52 wounded.
But Colonel-General Anatoly Nogovitsyn rejected Georgian claims that up to 50 Russian jets had bombed Georgia overnight.
London and Washington both backed their ally Georgia, which has set its sights on NATO and EU membership. British Foreign Secretary David Miliband condemned Moscow for bombing targets "well beyond" South Ossetia and said there was widespread concern about the escalating violence.
But Russia, angered by what it saw as an unwarranted Georgian attack on South Ossetia last week and determined to avoid Tbilisi attacking another pro-Russian separatist area, was in no mood for compromise.
Moscow issued an ultimatum to over 1,500 Georgian forces stationed in the Zugdidi district near Abkhazia, a second separatist area west of South Ossetia, to disarm or face attack but Georgia swiftly rejected the demand.
Russia said it had boosted its forces in Abkhazia beyond normal levels, stationing more than 9,000 paratroopers and 350 pieces of armour there to "rule out a repetition of the situation Russian peacekeepers faced in Tskhinvali".
Moscow deployed yet more armour and troops across its southern border into North Ossetia on Monday.
A Reuters reporter said T-72 tanks and Hurricane multiple rocket launchers choked the road between Russia and Tskhinvali as military convoys headed south.
French Foreign Minister Bernard Kouchner, whose country holds the rotating presidency in the European Union, met Saakashvili on a mission to try to end the war. He was expected to go to Moscow on Monday evening.
After meeting Saakashvili, Kouchner said a "controlled withdrawal of troops" was his main priority. A Georgian government source said on Sunday 130 Georgian civilians and military personnel had been killed and 1,165 wounded, many because of Russian bombing inside Georgia. Russia denies hitting civilian targets.