U.S. President Georgia W. Bush talked tough, too, accusing the Russians of "bullying and intimidation," but neither he nor Rice said what the U.S. might do if Russia ignored them.
Russian President Dmitry Medvedev's press office had no information Friday night on whether he had signed the cease-fire agreement.
Even as Rice stood with Georgian President Mikhail Saakashvili in a show of solidarity, he asked, "Who invited the trouble here? Who invited this arrogance here? Who invited these innocent deaths here?"
Shaky and near tears following a difficult, nearly five-hour meeting with her, Saakashvili answered his own question: "Not only those people who perpetrate them are responsible, but also those people who failed to stop it."
Rice let that pass, focusing instead on the demand that Moscow immediately withdraw its forces.
"With this signature by Georgia, this must take place and take place now," she declared.
There was no immediate clue to the Russians' intentions a week after their tanks and bombers attacked Georgia in retaliation for Georgia's attempt to retake a disputed province by force.
Russian troops allowed some humanitarian supplies into the strategic city of Gori but otherwise continued their blockade.
Adding to the day's tensions was a top Russian general's comments that Poland's agreement to accept a U.S. missile interceptor base exposed the ex-communist nation to attack, possibly by nuclear weapons, the Interfax news agency reported.
The statement by Gen. Anatoly Nogovitsyn is theagainst the plans to put missile defense elements in former Soviet satellite nations.
The cease-fire document sets out no specific penalties or deadlines. It contains concessions to Russia that Saakashvili obviously found hard to swallow. Russia could retain peacekeeping forces in the separatist region of South Ossetia and another breakaway region, Abkhazia, and the forces would have a broader mandate in South Ossetia.
Even if Russia fully complies with the cease-fire, the Bush administration says there will be more consequences to come. Bush's advisers are settling on penalties that would be intentionally modest and subtle, such as continuing to exclude Russia's foreign minister from discussions among his counterparts in elite gatherings of the world's leading economies.
The idea is to give Moscow the diplomatic cold shoulder while offering face-saving leeway for Russia to turn away from a mentality the West sees as throwback to its empire days. Russia would then have motivation, and some wiggle room, to seek inclusion in Western economic, political and security institutions.
In Washington, Bush accused Russia of resorting to thuggery from another era. He insisted the United States will not abandon Georgia, a Western-leaning democracy on Russia's southern flank and once part of the old Soviet Union.
"Bullying and intimidation are not acceptable ways to conduct foreign policy in the 21st century," Bush said. "Only Russia can decide whether it will now put itself back on the path of responsible nations or continue to pursue a policy that promises only confrontation and isolation."
The peace pact was worked out earlier in the week by French president Nicolas Sarkozy and both sides had said they agreed to it.
Russian forces remained, however, and U.S. officials said the document would take effect once it was formally signed Friday. It tells both sides to pull their forces back to the positions they held before fighting broke out last week in South Ossetia.
Saakashvili's emotional tirade and the forceful words from Bush in Washington suggested that a week into the crisis, both leaders were reassessing how they got here.
"We will rebuild. We want them out. I want the world to know, never, ever will Georgia reconcile with occupation of even one square kilometer of its sovereign territory. Never, ever," Saakashvili said.
His leadership is founded on a close alliance with Washington that has always exasperated Moscow.
Bush gave his most sustained explanation of U.S. action during the crisis, saying the conflict is about much more than a small country far away. Bush made clear the real fight is about the power and ambition of nuclear-armed Russia after the collapse of the Soviet Union and Russia's resurgence as an energy dynamo.
"The Cold War is over. The days of satellite states and spheres of influence are behind us," Bush said at the White House, before a vacation delayed by the crisis. "A contentious relationship with Russia is not in America's interest, and a contentious relationship with America is not in Russia's interest."
Rice said the time had come "to begin a discussion of the consequences of what Russia has done. This calls into question what role Russia really plans to play in international politics."
Rice was flying to Texas, where she was to give Bush a firsthand account of her diplomatic mission.
Apparently concerned that her awkward press conference with Saakashvili had set the wrong tone, Rice spoke briefly on her own before leaving Georgia.
"It's obviously a very emotional time here in Georgia," she said after visiting wounded people in a hospital.
"It's clearly a very emotional time, but I think that it should still be seen that this was a productive day. I hope now that peace can return to Georgia and Georgians can return to a normal life."
Pentagon spokesman Bryan Whitman said Friday that 82 tons of humanitarian supplies have been delivered to Georgia so far in four aircraft flights. He said the U.S. military is planning to do another two flights each day through the weekend.
There are still roughly 100 U.S. military personnel in Georgia - ranging from military trainers to security personnel at the embassy. Some of the trainers are scheduled to leave because they are reservists and their tour is over, Whitman said.
"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.
The cease-fire requires Russia to withdraw its combat forces from Georgia but allows Russian peacekeepers to remain in the breakaway region of South Ossetia and conduct limited patrols outside the region.
A draft of the document did not commit Russia to respecting Georgia's "territorial integrity," but rather refers to Georgian "independence" and "sovereignty." That means Moscow does not necessarily accept that Georgia governs South Ossetia and a larger separatist territory, Abkhazia.
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. Those borders now include the two provinces where many Russian citizens and loyalists live.
The U.S. and its allies had been pushing for Russia to agree to restore the situation to the status quo 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, ideally within days.
In addition to the cease-fire document, Rice carried with her a letter signed by Sarkozy that clarifies the special security measures that Russian peacekeepers will be allowed to take on Georgian soil, officials said.
"These clarifications are meant to protect Georgian interests," she said.
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.
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.