Georgia has pledged to crush a rebel group in a volatile gorge in the breakaway Abkhazia region.
Its troops are continuing an operation in the Kodori gorge to disband militia leader Emzar Kvitsiani.
At least four government soldiers have been injured since the operation was launched on Tuesday, according to reports in Georgia's media.
Abkhaz troops are on alert, and Russia has warned Tbilisi it will not tolerate an armed conflict along its border.
In Brussels, Nato Secretary General Jaap de Hoop Scheffer called for a peaceful resolution of the violent stand-off.
A Georgian government spokesman said the rebels refused an ultimatum to surrender and opened fire against Georgian special forces who entered the gorge.
The spokesman told civilians in the area to stay away from the rebels, because, as he put it, "the ground will burn beneath their feet".
Officials in Tbilisi expressed confidence that the operation would be over "in several hours".
They say the insurrection led by Emzar Kvitsiani, former governor of the Kodori gorge, is backed by Russia.
They say Russia is looking for an excuse for military intervention in Georgia.
Moscow denies any role in the uprising.
Russia has put its troops in the area on alert, condemning the Georgian deployment as a "serious violation of the 1994 Moscow ceasefire agreement", which halted fighting between Georgian and Abkhaz separatist forces.
The unrecognised Abkhaz government has also protested against the Georgian move in the strategically important gorge - the only part of Abkhazia still under nominal Georgian government control.
Georgia has demanded that Russia withdraw its troops from Abkhazia and another breakaway region - South Ossetia.
Moscow insists that its troops are peacekeepers, needed to prevent a resumption of hostilities.
Abkhaz rebels drove Georgian troops from the region in 1993.