On the ground in Georgia, the ceasefire seems to be holding, with Russian troops remaining in position around the strategic city of Gori, 20 miles from the break-away region of South Ossetia where the conflict erupted, reports CBS News national correspondent Thalia Assuras.
Humanitarian aid, some from the United States, continues to filter into the area in an effort to help more than 100,000 displaced civilians.
But on the diplomatic front, tensions remain high, Assuras reports. After a meeting in Tbilisi, Germany's chancellor Angela Merkel declared support for Georgia's entry into NATO, a statement likely to rankle the Kremlin. And Georgia's president continued talked tough.
Senior U.S. officials took a hard line too, declaring that Russia's actions have seriously strained relations with the West - and again accusing the Kremlin of reverting to a cold war stance.
Medvedev suggested that Russian forces could remain in separatist South Ossetia, the focus of the conflict. Georgian President Mikhail Saakashvili said his country will not give up that breakaway region or another separatist province, Abkhazia.
"Georgia will never give up a square kilometer of its territory," Saakashvili told a news conference alongside Chancellor Merkel, the latest Western leader to visit Tbilisi and offer support for a country at the center of deepening tensions between Russia and the West.
"I expect a very fast, very prompt withdrawal of Russian troops out of Georgia," Merkel said in a courtyard at Saakashvili's official residence. "This is an urgent matter."
As she spoke, Russian tanks and troops continued to roam freely across a wide swath of Georgia and desperate Georgian refugees in Gori were seen shoving and shouting in an attempt to get bread.
Saakashvili alleged that Russian forces, far from withdrawing, had moved closer to the capital Saturday and - some of his trademark bluster still intact - vowed to defend Tbilisi if necessary. He also accused Russia of ethnic cleansing and said Georgia would not accept a future presence of Russian peacekeepers.
Medvedev told French President Nicolas Sarkozy that Russian forces would begin their withdrawal Monday, moving toward South Ossetia and a security zone that roughly coincides with its borders, according to the Kremlin.
But he stopped short of promising they would return to Russia, suggesting that Russia could maintain a sizable force in South Ossetia. That would likely fuel fears that Russia could seek to annex the region, which - like Abkhazia - broke from government control in the 1990s and has declared independence.
Sarkozy warned Medvedev on the phone Sunday that Russia would face "serious consequences" if it did not begin the pullout - a sentiment echoed in Washington.
"I hope this time he'll keep his word," U.S. Secretary of State Condoleezza Rice said after Medvedev's statement.
U.S. Defense Secretary Robert Gates said Russia was showing signs of returning to its authoritarian past - a development that will require the U.S. to re-evaluate the strategic relationship between the superpowers.
Georgia, bordering the Black Sea between Turkey and Russia, was ruled by Moscow for most of the two centuries preceding the 1991 breakup of the Soviet Union. Under Saakashvili, Georgia has sought NATO membership and has emerged as a proxy for conflict between an emboldened Russia and the West.
The EU-backed cease-fire agreement calls for Georgian and Russian troops to withdraw to the positions they held before fighting broke out Aug. 7.
Russian troops still have a stranglehold on Georgia because they control the main highway running through the country and surround the central strategic city of Gori, the western city of Senaki and the Senaki air base.
Russian troops were entrenched on a hill after building ramparts around tanks and posting sentries near Igoeti, a central Georgia town only 30 miles west of Tbilisi.
There were several Russian checkpoints Sunday on the road between Igoeti and Gori, a central city not far from South Ossetia. Some armored vehicles stood off the side of the road, camouflaged with cut branches.
There were a few military vehicles but no longer any tanks at the checkpoint at the entrance to Gori, less fortified than in previous days.
In Gori itself, there was a light presence of Russian troops and a few tanks. Virtually all shops were closed and the streets almost empty, save for clusters of people, many from outlying villages, who gathered around aid vehicles and a basement bakery.
People shouted and shoved as they tried to grab loaves of bread and boxes. A few women appeared hysterical at the shifting nature of the food distribution from handouts to a registration system.
The Russians also controlled the Black Sea port city of Poti and the road north to Abkhazia.
Georgia's Foreign Ministry accused Russian army units and separatist fighters in Abkhazia of taking over 13 villages and the Inguri hydropower plant, shifting the border of the Black Sea province toward the Inguri River. Russia confirmed Sunday that its peacekeepers were in control of the western power plant.
The villages and plant are in a U.N.-established buffer zone on Abkhazia's edge, and it appeared the separatists were bolstering their control over the zone after forcing Georgians out of their last stronghold in Abkhazia last week.
"No matter what happens, we will never reconcile with the fact of annexation or indeed separation of parts of territory from Georgia; with the attempt to legalize ethnic cleansing; and with the attempts to bring Georgia to its knees and undermine our democratic system," Saakashvili said.
The West agrees that Georgia must not be broken up divided, Merkel said.
"Georgia is a sovereign state and the territorial integrity of the state must be provided for," she said.
She stressed German support for Georgia's NATO aspirations but said she did not know when that would happen. Merkel also suggested NATO could help rebuild the tattered Georgian military.
NATO offered Georgia assurance in April that it would eventually join NATO, but declined to offer it a blueprint for membership, in part because of fears in Germany and other European nations of angering Russia, a major EU energy supplier.
Russian Foreign Minister Sergey Lavrov said Thursday that Georgia could "forget about" getting the two regions back. On Saturday, he said that Russia will boost its peacekeeping force in South Ossetia and will not withdraw its other troops until further security measures are taken.
In Tbilisi, the faithful went to church Sunday, praying and lighting candles in the city's Holy Trinity Cathedral, a Georgian Orthodox church.
"I wish peace for my country and for our children. We do not want to live in fear," resident Ia Kvirkvelia told an AP television news crew.
A large anti-Russian banner hung Sunday in front of the Parliament building in central Tbilisi: "No war, Russia go home."
In Italy, Pope Benedict XVI called for the immediate creation of a humanitarian corridor to speed aid to refugees and for all sides to respect the rights of ethnic minorities.
The conflict erupted after Georgia launched a massive barrage Aug. 7 to try to take control of South Ossetia. The Russian army quickly overwhelmed its neighbor's forces and drove deep into Georgia, raising fears that of a long-term Russian occupation.
Russia views the growing relationship between the U.S. and Georgia as an encroachment on its traditional sphere of influence. The fighting came amid U.S. efforts to close a deal on a missile shield based in former Soviet satellites in Europe.
By Associated Press writer Christopher Torchia. The AP's David Nowak, Steve Gutterman and Jill Lawless in Moscow, Michael Fischer and Matti Friedman in Tbilisi, Georgia, and Deb Riechmann in Crawford, Texas contributed to this report.