TBILISI, Georgia (CNN) -- Georgia\'s president says he has signed an international-brokered proposal for a cease-fire with Russia in their conflict over the breakaway province of South Ossetia.
Georgian troops on a tank in the city of Gori, which their president claims was attacked by Russia.
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President Mikheil Saakashvili said Monday that the proposal would be taken to Moscow by the French and Finnish foreign ministers.
"We are trying to stop this as soon as possible," Saakashvili said during a conference call with Western journalists.
Saakashvili said that Georgian troops had downed "18 or 19" Russian warplanes, killed hundreds of Russian troops and repelled a Russian assault on the Georgian city of Gori.
He claimed Russia had 500 tanks and 25,000 troops inside Georgia. Watch aftermath of Russian strike »
A Russian defense ministry spokesman denied that Russian troops had entered Georgian territory outside of the breakaway regions South Ossetia and Abkhazia, and said only four planes had been lost.
French President Nicolas Sarkozy, the president of the European Union, will visit the capitals of both Russia and Georgia Tuesday in his diplomatic efforts to end the fighting, according to Saakashvili.
Sarkozy\'s office earlier said he would travel to Moscow to meet with Russian President Dimitri Medvedev, but it has not confirmed a stop in Tbilisi.
French Foreign Minister Bernard Kouchner and Finnish Foreign Minister Alexander Stubb were to make their way to Moscow on Monday evening after spending Sunday and Monday in Tbilisi meeting with Georgian officials.
Stubb said they had a proposal which included a "forceful way forward" to a cease-fire and withdrawal plan. Watch more on the victims of the fighting »
"I agreed with every point of it," Saakashvili said. "They are going now back to Moscow trying to convince the Russians to take the offer."
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A Georgian National Security Council official said the document signed by Saakashvili called for an unconditional cease-fire, a non-use of force agreement, a withdrawal of Russian troops from Georgian territory, including the South Ossetia region, and provisions for international peacekeeping and mediation.
Sources close to the delegation said the French and Finnish ministers, along with their Georgian counterpart, would visit Gori Monday afternoon to see first-hand damage caused by Russian airstrikes.
Russian Defense Ministry Colonel-General Anatoly Nogovitsyn said some Georgian troops remained in South Ossetia but they were being driven out.
"At the moment, our troops are pushing out, capturing and disarming groups of Georgian law enforcement agencies which have been surrounded in the capital of South Ossetia," Nogovitsyn said. Watch Georgia\'s president run for cover »
Nogovitsyn said Russian forces "are not going beyond" the borders of South Ossetia.
"This is a matter of principle," he said. "The 1992 treaty which Georgia signed, among others, clearly defines the limits of responsibility of the Russian peacekeeping contingent, and is doesn\'t have any tasks of invading the Georgian territory.
Russia controls the sky
The skies over the breakaway regions and Georgia belonged to the Russians, he said, as the Georgian air force was not flying.
They had "inflicted damage on operational systems, troops and military facilities of Georgia," but Nogovitsyn denied Russian bombers had attacked a civilian radar installation at the Tbilisi International Airport.
A Georgian Foreign Ministry statement said "several dozen Russian bombers" were over Georgian Monday afternoon "intensively bombing Tbilisi, Poti, villages in Adjara, and elsewhere."
"Overnight, as many as 50 Russian bombers were reported operating simultaneously over Georgia, targeting civilian populations in cities and villages, as well as radio and telecommunications sites," the statement said.
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Colonel-General Nogovitsyn repeated an earlier charge that Georgian troops were engaged in genocide against civilians in South Ossetia, which he said he could "prove to the media."
"During their mop-up operations in South Ossetia, Georgian commandos have thrown hand grenades into the basements where civilians were hiding," he said. "That\'s what we call genocide."
South Ossetia\'s capital, Tskhinvali, lay in smoldering ruins after four days of fighting between Georgian and Russian forces. Each side accused the other of killing large numbers of civilians. Russia said at least 2,000 people had been killed in Tskhinvali.
Georgia began withdrawing its forces from Tskhinvali early Sunday.
Georgia, a pro-Western ally of the U.S., is intent on asserting its authority over South Ossetia and Abkhazia, both of which have strong Russian-backed separatist movements.
The situation in South Ossetia escalated rapidly from Thursday night, when Georgia said it launched an operation into the region after artillery fire from separatists killed 10 people. It accused Russia of backing the separatists.
South Ossetia, which has a population of about 70,000, is inside Georgia but has an autonomous government. Many South Ossetians support unification with North Ossetia, which would make them part of Russia.
Russia supports the South Ossetian government, has given passports to many in South Ossetia, and calls them Russian citizens.