Medvedev told World War Two veterans in the Russian city of Kursk, "If anyone thinks that they can kill our citizens and escape unpunished, we will never allow this. If anyone tries this again, we will come out with a crushing response."
He added, "We have all the necessary resources, political, economic and military. If anyone had any illusions about this, they have to abandon them."
Medvedev was speaking shortly before Russia's deputy chief of general staff, Colonel-General Anatoly Nogovitsyn announced that the withdrawal had begun, although Georgian authorities have denied any such occurance.
"The Russians aren't withdrawing, they are in the same places. They are in Senaki, Khashuri, Zugdidi and Gori," Shota Utiashvili, a Georgian Interior Ministry official, told Reuters.
Russian troops with armoured cars mounted checkpoints on a major Georgian highway, ahead of the promised withdrawal from parts of the country under an international ceasefire plan.
In the central Georgian town of Gori, a reporter saw armoured personnel carriers bringing what looked like ration boxes out to checkpoints.
One soldier from Volgograd, asked how long he would be there, replied: "We don't know. Our orders are to stay here."
Russia mounted its biggest military deployment outside its borders since the 1991 collapse of the Soviet Union after Georgia sent a force on Aug. 7-8 to try to recapture the rebel, Moscow-backed province of South Ossetia.
The European Union and the United States, wary of a drift back into conflict if there are delays, are pressing Moscow to finish the pullout quickly.
Both Brussels and Washington want to see international observers on the ground quickly to monitor the pullout but no arrangements for this have yet been made.
The United Nations said a first aid convoy managed to enter Gori on Sunday and that while buildings did not appear to be badly damaged, there were "clear signs of massive looting".
Georgian television showed pictures of Russian forces moving out of the western Georgian town of Senaki, but it was not clear if this was part of the promised larger withdrawal.
Georgian President Mikheil Saakashvili, in a shift from previous statements condemning Russians as "21st century barbarians" bent on ethnic cleansing, called on Monday for talks with Moscow.
"I appeal to you that after your armed forces leave Georgian territory, to start serious thinking and discussions about further negotiations, a further search for ways (to conduct) relations in order not to sow discord between our countries for good," Saakashvili said in the broadcast.
Russian leaders have condemned Saakashvili as a dangerous "maniac" and have suggested privately that there is no need to speak to him because his own people will topple him before long.
Accusations of 'genocide'
The 10-day confrontation around South Ossetia has killed more than 170 Georgians, dealt a blow to the Georgian military, damaged the country's economy, disrupted road and rail links and drew Western criticism of Saakashvili's handling of the crisis.
Washington has strongly backed its close ally Georgia and accused Russia of "bullying" its small, former Soviet vassal.
Russia and Georgia have accused each other of attempted genocide during the conflict, though some humanitarian organisations have questioned whether the term is appropriate.
Russia says some 1,600 people were killed in the initial Georgian attack on the South Ossetian capital of Tskhinvali, a figure which has not been independently confirmed.
Georgia accuses Russian and irregular forces of levelling Georgian villages around the South Ossetian capital Tskhinvali.
From Tskhinvali, the separatist leader Eduard Kokoity told Reuters in an interview that he wanted a permanent Russian military base in South Ossetia and pledged never again to accept international observers in his territory.
"They fled meanly like traitors from South Ossetia just before the shooting started," he said. "...We have no confidence in these international observers, in these people who corrupt the truth."
Russia has sent in aid to South Ossetia to help thousands of displaced people and help restore ruined infrastructure, water and sanitation facilities but international organisations have not been granted the same access.
The International Red Cross complained on Monday that its president, Jakob Kellenberger, had not been given permission to enter South Ossetia to assess the situation.
The Russians have not set a deadline for completion of the military pullout, saying it depends on stability in Georgia.
The six-point peace plan foresee a prompt withdrawal of Russian forces from 'core Georgia' - the areas outside South Ossetia and a second Russian-backed separatist province of Abkhazia - but the West will also be looking for Russian troops to cut back their numbers quickly in South Ossetia itself.
The conflict has rattled the West, which draws oil and gas through pipelines across Georgian territory from the Caspian region - a route favoured because it bypasses Russia.
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