Also, President George W. Bush demanded that Russia leave Georgia, saying the people there have cast their lot with the free world and "we will not cast them aside."
In a statement Friday at the White House, the president said the Cold War is over and that a contentious relationship with the United States is not in Russia's interests. He said that "bullying and intimidation are not acceptable ways to conduct foreign policy in the 21st century."
Russia's President Dmitry Medvedev shot back, saying Georgia's two separatist regions are unlikely to ever be parts of the country again.
At a news conference with German Chancellor Angela Merkel in the resort town of Sochi, Medvedev said that although Russia respects the principle of territorial integrity, "After what happened, it's unlikely Ossetians and Abkhazians will ever be able to live together with Georgia in one state."
In Tbilisi with the cease-fire document, Rice said the immediate goal is to get Russian combat forces out of Georgia and more difficult questions about the status of the country's separatist regions and Russia's presence there can be addressed later.
"The United States would never ask Georgia to sign onto something where its interests were not protected," she told reporters aboard her plane as she flew to the Georgian capital from France where she met French President Nicolas Sarkozy who brokered the cease-fire.
"This is not an agreement about the future of Abkhazia and the future of South Ossetia," Rice said, referring to the two flashpoint areas. "This is about getting Russian troops out."
Mr. Bush, preparing to travel to his Texas ranch, said in his statement on the White House grounds that he'll keep in close touch with both Secretary of Defense Robert Gates and Rice.
Meanwhile, Rice will be consulting with pro-Western Georgian President Mikhail Saakashvili about details of the cease-fire, which will require Russia to withdraw its combat forces from Georgia but allows Russian peacekeepers to remain in South Ossetia and conduct limited patrols outside the region.
The draft document also does not commit Russia to respecting Georgia's "territorial integrity," but rather refers to Georgian "independence" and "sovereignty," meaning Moscow does not necessarily accept that South Ossetia and Abkhazia, are Georgian.
Officials say the eventual status of the two areas will be worked out under existing U.N. Security Council resolutions which recognize Georgia's international borders and Abkhazia and South Ossetia as Georgian.
The U.S. and its allies had been pushing for Russia to agree to restore the situation in Georgia to the "status quo ante," or how it stood before Georgian troops moved into South Ossetia last week prompting Russia's severe response and seven days of bloodshed.
Now they have been forced to back down on the key issues of the mandate of Russian peacekeepers in South Ossetia, which did not previously include outside patrols, and the territorial integrity question, which Russia ostensibly accepted before but no longer does.
U.S. officials concede the agreement is not perfect but maintain it will get Russian combat troops out of Georgia, hopefully in a matter of days.
"It will be a major accomplishment for Georgia to get the Russians out of their country and back effectively to the status quo ante," Rice said. "I think that will be a major accomplishment."
"These clarifications are meant to protect Georgian interests," she said.
If agreed, the cease-fire would allow Russian peacekeepers who were in South Ossetia before the fighting broke out to stay and to patrol temporarily in a strip of up to 6.2 miles, or 10 kilometers, outside, officials said.
"Any measures that they are allowed to take have got to be of a very limited nature for a very limited period of time," Rice said.
Officials say the expanded mandate would end as soon as a team of international monitors could be sent to observe, something they believe can be done in weeks.
Russian troops and Georgian troops briefly patrolled Gori together Thursday before relations between the sides broke down and the Georgians left. At least 20 explosions were heard later near Gori, along with small-arms fire. It was not clear whether it was renewed fighting or the disposal of ordnance from a Georgian military base.
Gori, battered by Russian bombing before Tuesday's cease-fire, lies on Georgia's main east-west road only 60 miles west of Tbilisi.
Terrified Georgians had to flee their village near Gori on foot, they said, because rampaging militias from South Ossetia are burning homes and farms, killing people and livestock, reports CBS News correspondent Mark Phillips.
Amid rising tensions with Russia over the situation in Georgia, Rice also said Thursday she would travel to Poland soon, possibly next week, to sign a missile defense agreement that Moscow vehemently opposes.
U.S. and Polish negotiators reached a deal on Thursday to deploy American interceptors in Poland as part of a European missile shield the United States plans. Under another agreement, a radar tracking station will be located in the Czech Republic.
and the agreement with Poland is bound to infuriate the Kremlin.
Rice was all smiles as she talked about it on Thursday. "I look forward to going to Poland to sign that agreement soon," she said. "It's important for the peace and security of the region, it's important for peace and security internationally."