Lavrov also said Russia would strengthen its peacekeeping contingent in South Ossetia, the breakaway Georgian region at the center of more than a week of warfare that has sharply soured relations between Moscow and the West.
The cease-fire deal, signed a a day earlier by Georgian President Mikhail Saakshvili after lengthy talks with Secretary of State Condoleezza Rice, calls for both Russian and Georgian forces to pull back to positions they held before fighting erupted Aug. 8.
Georgia launched a massive barrage to try to take control of the Russian-backed separatist region of South Ossetia. The Russian army quickly overwhelmed the forces of its small U.S.-backed neighbor and Moscow's troops drove deep into Georgia.
The Russian seizure of territory raised fears that Moscow was aiming for a permanent occupation of the country that once was part of its empire.
President Bush told reporters at his ranch Saturday that Russian President Dmitry Medvedev's signing of the cease-fire plan was an important development - "a hopeful step."
"Now, Russia needs to honor the agreement and withdraw its forces and, of course, end military operations," in Georgia.
Lavrov, the foreign minister, confirmed that Medvedev signed the cease-fire and ordered its implementation. But he suggested there would be no immediate withdrawal. He said Russian peacekeepers must strengthen security.
"As these additional security measures are taken, the units of the Russian armed forces that were sent into the zone of the South Ossetian conflict ... will be withdrawn."
Asked how much time it would take, he responded: "As much as is needed."
The crisis has chilled relations between the United States and Russia. The fighting comes as the U.S. is sealing the deal on a missile shield in Europe - an issue already unraveling ties between the two former Cold War foes.
Poland and the U.S. signed a deal Thursday for Poland to accept a missile interceptor base as part of a system the U.S. says is aimed at blocking attacks by adversaries such as Iran. Moscow feels it is aimed at Russia's missile force.
Keeping up the diplomatic pressure, Rice planned to go to Brussels next week for meetings with the foreign ministers of NATO allies and European Union officials.
Lavrov was not specific about the security measures, but suggested they would be limited mostly to South Ossetia, not Georgia proper. He accused Georgia of undermining security, citing the Russian military's claim that it had averted an attack on a highway tunnel by stopping a car laden with grenade launchers and ammunition.
"We are constantly encountering problems from the Georgian side, and everything will depend on how effectively and quickly these problems are resolved," he said.
Georgia, meanwhile, claimed that Russian forces blew up a railroad bridge Saturday. Russia denied it.
Russian soldiers earlier dug shallow foxholes in the center of Igoeti, some 30 miles from Tbilisi, but abandoned them later Saturday. But tanks and troops were still in place on a hillside on the edge of Igoeti, and there was no immediate signs of a pullout from the strategic central city of Gori, about 20 miles up the road.
Russian troops effectively control the main artery running through the western half of Georgia, because they surround Gori and the city and air base of Senaki in the west. Both cities sit on the main east-west highway that slices through two Georgian mountain ranges.
Controlling Senaki also means the Russians are blocking access to the Black Sea port city of Poti and the road north to Abkhazia.
AP reporters have seen Russian troops there for days but noted a growing contingent Saturday and artillery guns and tanks pointed out from the city, which they appear to be using as a base for their sorties elsewhere in western Georgia.
Even if Russian forces do withdraw from Georgia proper, Moscow appears likely to maintain strong control over South Ossetia, whose leaders claim independence from Georgia and have sought to join Russia by merging with a neighboring Russian region also populated largely by ethnic Ossetians.
Lavrov said there is "no ceiling" on the number of peacekeepers Russia can have in South Ossetia.
He said Russia is in talks about outside monitors and has suggested raising the number of international observers for South Ossetia.
But he said any "international mechanism" for South Ossetia must back the work of Russian peacekeepers long stationed in the province, indicating that Georgia would not be able to restore its peacekeeping contingent there.
"These questions are not decided by Condoleezza Rice or somebody else. They are decided first of all by the side that has suffered in the conflict," Lavrov said. "What peacekeepers from what countries are needed for the people of South Ossetia to feel comfortable is a primarily up to the people of South Ossetia."
Lavrov also said the cease-fire deal Saakashvili differed from the one signed by Medvedev, lacking the introductory portion. While the difference appeared largely to be a technicality, it was one that either side might potentially cite if it wanted to abandon the deal.