Moscow said it had begun a military pullback from Georgia on Monday and President Dmitry Medvedev promised a "crushing response" to any future attack on Russian citizens.
The White House urged a Russian withdrawal "without delay", the latest in a series of similar appeals which have had no visible impact as Moscow has declined to set a pullout timetable.
A senior U.S. official said there were no signs yet that the Russian forces had begun to leave. Georgia said they were broadening their presence.
"Quite the opposite. They are spreading out to other regions," Deputy Foreign Minister Giga Bokeria said.
Russia's crushing defeat of Georgia—its first military campaign outside its borders since the 1991 collapse of the Soviet Union—has damaged ties with Washington and raised concerns over the stability of a key oil and gas transit state.
Russia responded with overwhelming force after Georgia sent its military on Aug. 7-8 to try to recapture the rebel, Moscow-backed province of South Ossetia.
In a show of defiance, Medvedev said: "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. We have all the necessary resources, political, economic and military," a stern-looking Medvedev told World War Two veterans in the Russian city of Kursk.
He later flew to Vladikavkaz, near the border of the conflict zone of South Ossetia, to hand out medals to soldiers who took part in the operation.
No Exact Date
In Moscow, the Russian General Staff told a daily briefing that Russian troops had begun their pullout from the conflict zone, though there was no independent verification of this.
"I can say for certain when the New Year will come but I cannot give an exact date for the withdrawal of our troops from the conflict area yet," said Col.-General Anatoly Nogovitsyn. "I can only say that we will not be leaving as fast as we came".
Georgia accused the Kremlin's forces of blowing up its weapons and ammunition dumps near the western town of Senaki—modernized to NATO standards—as they withdrew.
(Russian troops are expected to withdraw from Georgia. Watch the accompanying video for more...)
"They are destroying everything and then pulling out of these places," Interior Ministry official Shota Utiashvili said. "If they call this a pullout, then I do not understand the meaning of the word."
A Reuters journalist in Senaki said he heard three loud explosions but was not allowed to enter the area. Explosions were also heard in the Gori area of central Georgia, though there were no reports of fighting.
Russian commanders accused Georgia of wrecking a planned prisoner exchange and continuing to mount isolated sniper and sabotage attacks on its positions.
"We are aware that the Georgian side can undertake provocative actions at any moment against our troops as well as the civilians," Nogovitsyn said. "We can't rule out the use of Slavic-looking people, dressed like Russian military, for provocations and sabotage".
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".
The International Committee of the Red Cross complained that its president had not been given access to South Ossetia for a fact-finding mission.
Georgian President Mikheil Saakashvili again attacked Russia in a television address for "senselessly looting, robbing, stealing, destroying and blowing things up" but said that after Moscow's occupation ended, there should be talks.
"I appeal to you, 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.
Russian leaders have branded him a dangerous "maniac" and suggested privately that there is no need to speak to him because his own people will topple him before long.
In the latest bitter verbal attack on him, Medvedev told Russian soldiers: "There are political freaks who are ready to kill innocent people for their political reasons."
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 and disrupted road and rail links.
Washington has strongly backed its close ally Georgia and accused Russia of "bullying" its small ex-Soviet vassal.
But some European powers have been critical of Georgia's behaviour in launching the assault on South Ossetia.
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.
From Tskhinvali, the separatist leader Eduard Kokoity told Reuters in a telephone interview that he wanted a permanent Russian military base in South Ossetia and pledged never again to accept international observers in his territory.
"South Ossetia will never be part of Georgia," he said.