Also on Saturday a senior Georgian official said by telephone that Russian bombers were flying over Georgia and that the presidential offices and residence in Tbilisi had been evacuated. The official added that Georgian forces still had control of Tskhinvali.

Image Georgian soldiers near a bombed building in Gori on Saturday. Credit... Gleb Garanich/Reuters

Neither side showed any indication of backing down. Prime Minister Vladimir V. Putin of Russia declared that “war has started,” and President Mikheil Saakashvili of Georgia accused Russia of a “well-planned invasion” and mobilized Georgia’s military reserves. There were signs as well of a cyberwarfare campaign, as Georgian government Web sites were crashing intermittently during the day.

The escalation risked igniting a renewed and sustained conflict in the Caucasus region, an important conduit for the flow of oil from the Caspian Sea to world markets and an area where conflict has flared for years along Russia’s borders, most recently in Chechnya.

The military incursion into Georgia marked a fresh sign of Kremlin confidence and resolve, and also provided a test of the capacities of the Russian military, which Mr. Putin had tried to modernize and re-equip during his two presidential terms.

Frictions between Georgia and South Ossetia, which has declared de facto independence, have simmered for years, but intensified when Mr. Saakashvili came to power in Georgia and made national unification a centerpiece of his agenda. Mr. Saakashvili, a close American ally who has sought NATO membership for Georgia, is loathed at the Kremlin in part because he had positioned himself as a spokesman for democracy movements and alignment with the West.