MOSCOW — Russian troops poured into Georgia Saturday as fighter jets unleashed bombs across the country, ratcheting up fears that a war has begun on Europe's border.

Russian airborne troops reached Tskhinvali, the capital of the breakaway Georgian territory of South Ossetia, where fierce fighting was reported and both sides claimed to have "liberated" the city. Russian state media reported some 100 military transport flights were planned to bring more units to the fray.

Earlier in the day, Russia Foreign Minister Sergei Lavrov said that about 1,500 people had been killed in the fighting.

The Russian ambassador to Georgia, Vyacheslav Kovalenko, upped that figure to 2,000, according to Interfax, a state newswire. Those figures could not be confirmed and were considerably higher than estimates by Georgia's government.

Georgian soldiers had tried to seize Tskhinvali, in north Georgia, on late Thursday and Friday to end the long-standing conflict between the country's government in Tblisi and the breakaway region. Russia, which backs the South Ossetians, scrambled troops in response.

On Saturday, the Georgian government said it was in a state of war and declared martial law.

At least 15 Russian peacekeepers had been killed and some 150 injured, according to Russian authorities. The Russian military confirmed to state media that two of its planes had been shot down over Georgia; Georgian officials asserted the real number was between five and 10.

Complicating the situation, a separate set of Russian-backed separatists from the area of Abkhazia, in Georgia's west, launched rocket strikes at Georgian military targets, an unnamed Abkhaz military source told Interfax.

"The situation continues to deteriorate," Lavrov said, accusing Georgia of razing whole villages in what he said amounted to "ethnic cleansing."

The rhetoric against Georgia has increasingly shifted from South Ossetian officials to the Kremlin, signaling that the battle was taking on far larger proportions.

During the past week, 34,000 refugees have fled to Russia from South Ossetia, Russian Prime Minister Vladimir Putin said at a press conference Saturday in Vladikavkaz, which is in North Ossetia just over the Russian border from South Ossetia.

The fact that Putin made a surprise visit there from Beijing, where he had been attending the Olympic Games the day before, underscored how seriously Russia is taking the matter. Putin is widely viewed as the heavier hand of the government, a man more suited than President Dmitry Medvedev at delivering a crushing blow.