GORI, Georgia – Russia pressed its invasion of Georgia by land, sea and air for a third day Sunday, striking far beyond contested South Ossetia as the Kremlin brushed aside a cease-fire offer and disputed Georgia's claim to have pulled its forces out of the rebel enclave.

Russian jets bombed Tbilisi, the Georgian capital, hitting civilian housing, military bases, factories and the international airport, according to Georgia officials. Also, Russian warships deployed off the Black Sea coast sank a Georgian missile boat that approached them, state-run Russian news media said.

A Russian official told the Associated Press that more than 2,000 people had been killed in South Ossetia since Friday; the figure could not be confirmed independently.

Russian troops and tanks, meanwhile, took control of Tskhinvali, the devastated capital of South Ossetia, according to Russian state-run media, and there were reports that an armored column tried to push out of the separatist enclave's boundary toward the city of Gori before being turned back by Georgian forces.

The military campaign also expanded as Russian troops entered Abkhazia, another separatist province.

Tensions between the United States and Russia sharpened as the Bush administration suggested that Russia's objective goes beyond securing South Ossetia to the ousting of President Mikhail Saakashvili, who has close ties to the United States and is seeking admission to NATO.

Russia denied the charge, repeating its position that it is obliged to stop "numerous war crimes" against civilians, many with Russian passports; end a "major humanitarian disaster"; and restore the situation to where it was before a Georgian military incursion Friday.

Two senior Western officials told the New York Times that it was unclear whether Russia intended a full invasion of Georgia, but that its aims could go as far as destroying its armed forces.

"They seem to have gone beyond the logical stopping point," one of the diplomats said.

Georgian police erected a checkpoint Sunday on the main road outside Gori and warned travelers that the situation around the city of 50,000, home to a major military base, was too dangerous. Russian warplanes strafed the city.

Scores of Georgian tanks and troop-carrying trucks roared down the road in the direction of the Russian advance in the predawn dark this morning. Dozens of other trucks were parked on the roadside, and truck-mounted missile launchers sat just outside Gori, where troops shouted for cars to turn off their lights.

Georgian troops moved last week to seize South Ossetia, a mountainous enclave bordering Russia, after clashes with separatist fighters. Moscow, saying Georgian forces killed Russian peacekeeping troops and civilians, responded by launching missile, artillery and air attacks and pouring hundreds of tanks, armored vehicles and troops across the border.

The tiny former Soviet republic, nestled between Turkey and Russia, is considered strategically important because it is located on key energy and trade routes to central Asia. Russia, which ruled Georgia for nearly two centuries before the Soviet Union's collapse in 1991, considers the region its backyard and opposes Georgia's admission to NATO.

Separatists began agitating for the secession of South Ossetia in the Soviet Union's waning days, igniting clashes with Georgian security forces that continued after Georgia became independent in 1991. Russia deployed peacekeeping troops in 1992.

Negotiations to resolve continuing disputes have made no progress.

As Russia moved more troops and tanks across its border into South Ossetia on Sunday, Saakashvili announced a withdrawal of Georgia troops from the province.

Georgia, he said, also was proclaiming a cease-fire, was ready to have it forces return to the positions they held before the fighting erupted and would sign an agreement for a peaceful resolution of the dispute.

But Russian officials rejected Saakashvili's claim of a troop withdrawal, saying that Georgian forces were continuing to fight. Russian Deputy Prime Minister Grigory Karasin, speaking to reporters in Moscow, said that Moscow would discuss "all further issues" once Georgia pulled out all of its forces and signed "a binding agreement on the non-use of force."

The United States and the European Union stepped up diplomatic efforts to end the bloodshed. Secretary of State Condoleezza Rice was in touch with senior Georgian, Russian and European officials. French Foreign Minister Bernard Kouchner, whose country is the current EU president, flew into Tbilisi on a peace mission only 30 minutes after the Russian airstrike on the international airport.

Tom Lasseter, the Moscow bureau chief for McClatchy Newspapers, reported from Gori, Georgia. Landay reported from Washington. Nancy Youssef of the McClatchy Washington Bureau, the Associated Press and the New York Times contributed to this report.