UNITED NATIONS — Six days after invading Georgia, and one day after President Bush scolded the Kremlin in harsh language for its “unacceptable” behavior, Russia declared that its military objectives in the pro-Western neighboring country had been achieved, and ordered its troops to halt their operations.

The announcement in Moscow by President Medvedev came just before his meeting with President Sarkozy, who visited the Russian and Georgian capitals yesterday in an attempt to end a war that, as Mr. Bush said, was launched in order to intimidate President Saakashvili and depose him.

Last night, Mr. Saakashvili agreed to the cease-fire as well, even though it did not include a Russian agreement to withdraw its troops from Georgian territory. Georgia’s U.N. ambassador, Irakli Alasania, told The New York Sun that Russian bombardment of targets in his country had not ceased even after Mr. Medvedev had agreed to the cease-fire, although troop movement stopped, he said. Mr. Medvedev said he had ordered troops to remain where they were and cease fire — unless targeting “hotbeds of resistance.”

“There is a text. It has been accepted in Moscow, it was accepted here in Georgia. I have the agreement of all the protagonists,” Mr. Sarkozy said at a late-night press conference in Tbilisi, after a long meeting with Mr. Saakashvili. Earlier in Moscow, the French president acknowledged that his six-point plan was designed to solve an “emergency situation” and was not meant to “solve all the problems.” At a late-night Tbilisi rally, Mr. Saakashvili defined the pact as “an agreement in principle.”

Russian officials yesterday essentially confirmed America’s contention that their goal was to unseat the Georgian leader. “Mr. Saakashvili can no longer be our partner, and it would be better if he went,” Russia’s foreign minister, Sergey Lavrov, told reporters.

Russia also said it had collected evidence to be used against the Georgian president in an international court. “A day of mourning” was declared by Moscow for today in which Russians would mark the “humanitarian disaster” in South Ossetia, where the fighting began last Thursday, and where according to Moscow 2,000 people have since been killed.

Georgia, for its part, instituted proceedings against Russia yesterday at the Hague-based International Court of Justice. It claimed that Russia and its allies in the breakaway region violated a convention meant to eliminate racism.

At the United Nations, diplomats started negotiating yesterday the “modalities to formalize” in a binding resolution the agreement Mr. Sarkozy reached in his capacity as the rotating president of the European Union, a European diplomat said. The agreement would require both sides to negotiate, the diplomat, who spoke on condition of anonymity, said: “The Russians can use whatever public rhetoric they want against Saakashvili, but as long as he is the elected president, they will have to deal with him.”

While Russia yesterday repeated its demand that all Georgian troops leave South Ossetia and Abkhazia, the two Russian-backed separatist regions of Georgia, Western officials stressed that those regions are part of Georgia’s nationally recognized territory. “I want to make very clear that the U.S. stands with the territorial integrity of Georgia, for the sovereignty of Georgia, that we support its democratically elected government and its people,” Secretary of State Rice told reporters at the White House.

The North Atlantic Treaty Organization’s secretary-general, Jaap de Hoop Scheffer, said Georgia remains “on track” for membership in the organization. “Allies reiterated in very strong terms the full respect necessary for the sovereignty and territorial integrity of Georgia,” he said. “And that is more than a phrase in a period of time when that territorial integrity is not respected by Russia.”

But it was unclear what effect the Russian show of force will have on other former Soviet republics vying for NATO membership — or on European members of the Brussels-based organization who would have to send troops to defend any member. One of the points in Mr. Sarkozy’s plan entails a peacekeeping contingency that would be charged with maintaining any Russian-Georgian agreement, diplomats here said, wondering whether European countries would be quick to volunteer for such a mission.

At least four journalists were reportedly killed during the battles in Georgia, and yesterday a former New York correspondent for the Israeli newspaper Yediot Achronot, Tzadok Yechezkeli, was critically injured while covering battles in the city of Gori.