Foreign Minister Sergey Lavrov also said Russia would strengthen its peacekeeping contingent in South Ossetia, the breakaway Georgian region at the center of more than a week of warfare that has sharply soured relations between Moscow and the West.
Lavrov signaled Russia's determination to set the rules for peace in an area where it has long viewed growing U.S. influence as an encroachment on its traditional sphere of influence. He said it is up to the South Ossetian people - and not U.S. Secretary of State Condoleezza Rice - to determine which countries can send peacekeepers and which cannot.
Russian soldiers earlier dug shallow foxholes in the center of Igoeti, some 30 miles from Tbilisi, but abandoned them later Saturday. But tanks and troops were still in place on a hillside on the edge of Igoeti, and there was no immediate signs of a pullout from the strategic city of Gori, about 20 miles up the road.
Officials said Medvedev signed a cease-fire deal - a day after his Georgian counterpart - setting the stage for a Russian withdrawal from positions in the former Soviet republic at the heart of rising tensions between an increasingly assertive Russia and a wary U.S. and Europe.
The agreement, signed Friday in Tbilisi by Georgian President Mikhail Saakashvili, calls for both Russian and Georgian forces to pull back to positions they held before fighting erupted Aug. 8.
Georgia had launched a massive barrage to try to take control of Russian-backed, separatist South Ossetia, prompting the Russian army to send in troops and tanks that quickly overwhelmed the smaller country's forces.
The Russian seizure of territory, including Gori and its positions in Igoeti, raised fears that Russia was aiming for a permanent occupation of the country that once was part of its empire. The cease-fire calls for Russian troops to pull back but allows limited Russian patrols in Georgia just outside the province.
Lavrov, the foreign minister, confirmed that Medvedev signed the cease-fire and ordered its implementation. But he suggested there would be no immediate withdrawal.
He said Russian peacekeepers must strengthen security. "As these measures of addition security are taken, the units of the Russian armed forces that were sent into the zone of the South Ossetian conflict ... will be withdrawn."
Asked how much time it would take, he responded: "As much as is needed."
Following the signing of the cease-fire agreement, though, Georgia's Foreign Ministry said Russian-backed separatists from the province of Abkhazia had seized 13 villages in Georgia and a power plant.
A ministry statement said Russian army units and separatist militants shifted the border of breakaway Abkhazia toward the Inguri River. It said they set up temporary administration in 13 villages and put the Inguri hydropower plant under separatist control.
The claim could not immediately be independently confirmed.
In Texas, U.S. President George W. Bush reminded Russia to abide by the cease-fire and said Moscow cannot lay claim to South Ossetia or Abkhazia, another Russian-backed separatist region in Georgia. The conflict and Russian remarks have raised fears in the West that Russia could absorb the two regions, which broke from Georgian government control in the early 1990s.
Lavrov was not specific about the security measures but suggested they would be limited mostly to South Ossetia, not Georgia proper. He accused Georgia of undermining security.
"We are constantly encountering problems from the Georgian side, and everything will depend on how effectively and quickly these problems are resolved," he said.
While Russian forces abandoned the center of Igoeti, they dug into positions on a hillside with a view of the area, possible defensive positions as their comrades withdraw.
In Gori, a crossroads city where Georgia says the presence of Russian forces has cut the country in half, two columns of military vehicles could be seen and there was no immediate sign of a pullout. Gori is on the same road as Igoeti, further from Tbilisi and closer to South Ossetia.
Even if Russian forces do withdraw from Georgia proper, Moscow appears likely to maintain strong control over South Ossetia, whose leaders claim independence from Georgia and have sought to join Russia by merging with a neighboring Russian region also populated largely by ethnic Ossetians.
Lavrov said there is "no ceiling" to the number of peacekeepers Russia can have in South Ossetia.
He said Russia is in talks about outside monitors and has suggested raising the number of international observers for South Ossetia.
But he said any "international mechanism" for South Ossetia must back the work of Russian peacekeepers long stationed in the province, indicating that Georgia would not be able to restore its peacekeeping contingent there.
"What peacekeepers from what countries are needed for the people of South Ossetia to feel comfortable is a primarily up to the people of South Ossetia," he said.
Lavrov also said the cease-fire deal Saakashvili signed differed from the one with Medvedev's signature, with Saakashvili's version lacking an introductory preamble. While that difference may appear to be a technicality, it could be one either side could cite if it wants to abandon the deal.
Georgia Accepts Russian Occupation
Demands by the U.S. that Russian troops pull out of Georgia are being pretty much ignored, and there is no sign that will change on any schedule other than one made in Moscow.
Ten days into the crisis, the few people left in the battered town of South Ossetia have begun to clean up what's left.
But CBS News correspondent Allen Pizzey reports that Russian armor and troops have not lifted their blockade of the breakaway region and - ceasefire deals notwithstanding - they are giving little indication that they're even thinking about moving out of the two regions of Georgia they now control.
"It is unlikely that Ossetians and Abkhazians will be able to live with Georgians in one state," Medvedev said after a meeting with German Chancellor Angela Merkel.
The U.S. is making a show of backing the Georgians, sending in more aid and promising support while acknowledging that the crisis is more than a local problem.
"The Russian attack on Georgia had profound implications and will have profound implications for Russia's relations with its neighbors and with the world," said U.S. Secretary of State Condoleezza Rice.
So far the Russians have shown no sign they are worried about what those implications might be. But the fact that it took five hours of negotiating just to get a ceasefire brokered by French president Nicolas Sarkozy clearly left the Georgian President exasperated - and he seems fed up both with being blamed for starting it and with what he sees as an inadequate international response.
"Who invited the trouble here?" Saakashvilli said. "Who invited this arrogance here? Who invited these innocent deaths here? Not only those people who perpetrated this are responsible but also those people who failed to stop them."
Whatever form a peace deal eventually takes, there seems little doubt that Moscow has got what it wanted, including sending a clear message that the Russian bear may have been quiet since the end of the Cold War but it was only hibernating.
A Situation Deemed "Complicated And Nervous"
Refugees have begun returning to the heavily damaged South Ossetian capital of Tskhinvali. On Saturday, many were sweeping up glass and debris from the fighting.
Teams of ethnic Georgians, some under armed guard, were being forced to clean the streets of South Ossetia's capital on Saturday. It was the first apparent evidence of humiliation or abuse of Georgians in the breakaway republic.
Mikhail Mindzayev, the interior minister for South Ossetia said police were cracking down on looters. Officers shot and killed two looters on Thursday, he said, and if they catch someone with a car or truck loaded with furniture or TV sets - and the driver does not seem to be the rightful owner - both the goods and the car will be burned.
Mindzayev described the situation in the city Saturday as "complicated and nervous." He said that there were many unexploded shells laying on the ground. He also accused Georgian agents of shooting at people in the city, a claim that could not be independently confirmed.
Russian Emergency Situations Ministry troops were erecting a camp near the scorched shell of the South Ossetian parliament building. For the first time in days, there were more cars on the street than tanks.
Farther south, the Russian presence in Gori is strategically critical: The city sits along Georgia's only significant east-west highway, allowing the Russians effectively to split the nation in two.
As in many parts of Georgia, aid has been slow to come. On Thursday, staff from the United Nations refugee agency and its World Food Program hoped to enter Gori to assess whether it was safe to deliver humanitarian aid.
The situation turned ugly. South Ossetian militiamen appeared, pointing weapons, and began shoving civilians and shouting at people to leave the area.
Georgian police had come to enter Gori but turned back when confrontation developed between the Russian military and the Georgian army.
On Friday, Russian military vehicles were blocking the eastern road into the city, although they allowed in one Georgia bus filled with loaves of bread.
Garadzim Tamgiashvili, 46, an unemployed electrician with graying red hair, said there was a lot of looting in the city by South Ossetians and Russians before the Russian military arrived. He said they killed civilians.
He said the Russian soldiers told him they planned to "give it to the Americans."
"We know this is a war between the West and Russia," he said.
Residents reported atrocities in the villages between Gori and Tskhinvali, the South Ossetian provincial capital. Outside Gori, an Associated Press reporter saw a burning wheat field. In the village of Tirdznise, the body of a Georgian soldier lay swollen in the heat.
But for the moment, Gori itself seemed to be a showcase. The Russian troops had stopped the looting, restored order.
One of the few younger women left was Iya Kinvilashvili, 30, the owner of a now-empty shop. Standing next to a church that has organized handouts of bread and flour, she said the Russians were behaving well.
"When is peace coming?" she asked. "We only want peace. We never wanted this war."