President Mikheil Saakashvili said Georgian troops would "unilaterally cease fire" after heavy fighting in its separatist region of South Ossetia.
"I want to address those people who are now shooting at our forces. I have just ordered - it is a very painful order - to cease fire. There are many casualties, both dead and wounded," Saakashvili said in a national televised address on Thursday.
Russian news agency Interfax cited Georgian media estimating casualties of 27 people on the Georgian side since fighting erupted over the weekend. Official sources would not confirm the death count.
Saakashvili's speech marked a conciliatory note as the fighting was accompanied by accusations of war-mongering between Georgia and Russia, which is closely allied with the separatist region.
"Georgia is a natural ally for Russia ... We need a real mediator," Saakashvili appealed in his speech.
"Immediately cease fire, please. We do not want to return fire. We have been tolerating this for so many years. Please, do not test the Georgian state's patience," he said.
Georgian officials had charged Russia earlier with arming the rebels.
The interior ministry reported one of its armoured personnel carriers had been blown up in an attack on the village of Avnevi.
News agency Interfax cited officials in the South Ossetia as saying Georgian forces were shelling villages in and surrounding its capital Tskhinvali, using mortars and artillery.
Separatists on the South Ossetian side said Georgia had deployed 27 rocket launchers and increased troops at the border.
South Ossetia claimed 18 people were injured in the overnight shootout Thursday. It reported six people dead in weekend clashes.
Local media cited witnesses saying they had seen military convoys on the route from western Georgia toward its two separatist regions of South Ossetia and Abkhazia.
Abkhaz President Sergei Bagapsh, wearing military fatigues, said in televised shots that he was holding troops on high alert in the wake of the fresh clashes.
The rebel regions fought wars of independence against Tbilisi in the early 1990s, but have not been recognized by any other country. Since 1994, they have been occupied by Russian peacekeepers under a UN deal.
Moscow is widely seen as backing the breakaway regions.
On Thursday, Russia accused Georgia of "irresponsible military action."
Acting Foreign Minister Grigory Karasin called on Tbilisi "to show the reasonable and weighed approach, to stop military preparations and power actions."
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