Russia's president promised to start withdrawing forces from positions in Georgia on Monday, but suggested they could stay in the breakaway region at the heart of the fighting that has reignited Cold War tensions.

Top American officials said Washington would rethink its relationship with Moscow after its military drive deep into its much smaller neighbor and called for a swift Russian withdrawal.

"I think there needs to be a strong, unified response to Russia to send the message that this kind of behavior, characteristic of the Soviet period, has no place in the 21st century," Defense Secretary Robert Gates said Sunday.

But neither Gates nor Secretary of State Condoleezza Rice would be specific about what punitive actions the U.S. or the international community might take.

Bolstered by Western support, Georgia's leader vowed never to abandon its claim to territory now firmly in the hands of Russia and its separatist allies, even though he has few means of asserting control. His pledge, echoed by Western insistence that Georgia must not be broken apart, portends further tension over separatist South Ossetia and Abkhazia.

• Click here to view photos of the conflict in Georgia.

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• Bush Accuses Russia of 'Bullying and Intimidation' in Georgia Conflict

• U.N. Reports Over 118,000 Georgians Have Fled Fighting

In Gori, a strategic central Georgia city, there were signs of a looser Russian grip -- and scenes of desperation as Georgians crowded around aid vehicles and grasped for loaves of bread.

Virtually all shops were closed and the streets almost empty, save for clusters of people who gathered around aid vehicles and a basement bakery.

Georgia hit the Russia-backed separatist region of South Ossetia with a massive barrage on Aug. 7. Russia responded by sending troops that advanced far into the Caucasus Mountain nation, raising fears of a long-term occupation of a country at the center of a power struggle between a resurgent Russia and the West.

The troops would leave, a Russian lawmaker said, "sooner or later."

"But how much time it will take, it depends, definitely, on how Georgians will continue to behave," said the lawmaker, Konstantin Kosachev, chairman of a Russian parliament foreign affairs committee.

Rice, who is flying to Europe on Monday to talk with NATO allies about what message the West should send to Russia, said Russia can't use "disproportionate force" against its neighbor and still be welcomed into the halls of international institutions.

"It's not going to happen that way," she said. "Russia will pay a price."

French President Nicolas Sarkozy warned Russia's president of "serious consequences" in Moscow's relations with the European Union if Russia does not comply with the cease-fire accord.

Later, Sarkozy said in an opinion article published on Le Figaro newspaper's Web site that if Russia did not "rapidly and totally" follow the pullout specified in the cease-fire, he would "have to call an extraordinary meeting of the Council of the European Union to decide what consequences to draw."

Medvedev had told Sarkozy that Russian troops would begin pulling back on Monday, headed toward South Ossetia. He stopped short of promising they would return to Russia.

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.

But Medvedev's silence on South Ossetia has fueled fears that Russia could annex the region, which -- like Abkhazia -- broke from Georgia government control in the 1990s and has declared independence. Getting Abkhazia alone would increase the length of Russia's Black Sea coast by more than 25 percent.

"Georgia will never give up a square kilometer of its territory," Georgian President Mikhail Saakashvili told a news conference alongside Germany's Angela Merkel, the latest Western leader to visit Tbilisi and offer support for the country he has led on a pro-Western path, seeking to shake off a history of domination by Moscow.

"I expect a very fast, very prompt withdrawal of Russian troops out of Georgia," Merkel said in a courtyard at Saakashvili's official residence. She reiterated a Western promise that Georgia will eventually join NATO, but said she could not say when that would happen.

As Merkel spoke, Russian tanks and troops continued to control a wide swath of Georgia, including the main highway running through the country, the strategic central city of Gori, the western city of Senaki and the Senaki air base.

On Sunday evening, Russian armored personnel carriers and tanks carrying military hardware traveled away from Senaki on a road that leads to Zugdidi, a city just outside Abkhazia -- possibly pulling out, though their destination was unclear.

In the western town of Zugdidi, residents took to the streets earlier Sunday to protest the Russian presence in Georgia. Demonstrators including politicians and Orthodox priests carried religious icons and sprinkled holy water as they marched, some holding red-and-white Georgian flags and pictures of Saakashvili.

"We are waiting for more support from other countries because this is not a war between Russian and Georgia, it's a war between civilization and barbarism," said Eldar Kbernadze, a member of Georgia's parliament who was among the protesters.

Saakashvili alleged that Russian forces, far from withdrawing, had moved closer to the capital Saturday and vowed to defend Tbilisi if necessary. He also accused Russia of ethnic cleansing and said Georgia would not accept the future presence of Russian peacekeepers.

A large banner hanging Sunday in front of the Parliament building in central Tbilisi read: "No war, Russia go home."

On the outskirts of the city, hundreds of Georgian refugees tended to children, tried to wash near open taps and sought shelter in tents in a makeshift refugee camp.

Georgia's government minister for refugees, Koba Subeliani, said there were 140,000 displaced people in Tbilisi and the surrounding area.

U.N. Secretary-General Ban Ki-moon is considering sending over several high-ranking U.N. officials, including monitors and a top official with the U.N. refugee agency, according to a U.S. official who spoke on condition of anonymity because he was not authorized to release the information.

Just 30 miles (48 kilometers) from Tbilisi, Russian troops were entrenched on a hill after building ramparts around tanks and posting sentries near Igoeti.

Elsewhere, the Russian checkpoint at the entrance to Gori was less fortified than in previous days. In the city, where buildings were blackened by fire from fighting or bombing, there was a light presence of Russian troops and a few tanks.

Marc Baldan, a surgeon from the International Committee of the Red Cross, which delivered some medicine and food in Gori, said the city's hospital was functioning and that drugs for heart disease, hypertension and diabetes, unavailable during the conflict, had been delivered.

"Each day looks better," he said. "But we still do not have the full picture."