A Georgian government minister says Georgian troops have captured five villages in the pro-Russian breakaway region of South Ossetia and are surrounding the region's capital, Tskhinvali.
Earlier reports said the city was under heavy shelling from Georgian-controlled areas.
A Georgian military commander says the government has launched an operation to, in his words, "restore constitutional order" to South Ossetia.
New fighting between Georgian forces and separatists broke out Thursday just hours after Georgian President Mikhail Saakashvili called for an immediate cease-fire.
Fighting earlier in the day killed at least 10 Georgian soldiers and civilians and wounded more than 20. The number of separatist casualties is unclear.
In a televised speech, Mr. Saakashvili again offered the separatists full autonomy within Georgia and said Russia could help guarantee that status.
It is not clear if Friday's planned talks between Georgian officials and South Ossetian separatists will still take place.
The United States called for an immediate end to the fighting. State Department spokesman Gonzalo Gallegos said the United States is in close contact with Russian and Georgian officials on the issue. Washington also is urging Moscow to press South Ossetian leaders to halt the violence.
South Ossetia declared independence from Georgia in the early 1990s, sparking fighting and the dispatch of Russian peacekeepers to the region.
Georgia accuses the peacekeepers of backing the separatists and has vowed to bring South Ossetia back under central government control. Some information for this report was provided by Reuters.