The head of Georgian peacekeepers in South Ossetia said the operation was intended to "restore constitutional order" to the region.
The Georgian Minister for Integration, Temur Yakobashvili, said Georgia's aim was not to take over the territory but to finish "a criminal regime".
Days of fierce conflict have raised fears of a new war in the volatile Caucasus.
In a televised address, Georgian President Mikhail Saakashvili earlier called for the bloodshed to end, but also warned the Russian-backed separatists not to try Tbilisi's patience.
A truce was later announced, with emergency talks set for Friday, but by nightfall, both sides were trading heavy fire.
Georgia accuses Russia of arming the South Ossetian authorities - who have been trying to break away since the civil war in the 1990s. Moscow denies the claim.
President Saakashvili has vowed to restore Tbilisi's control over South Ossetia and Abkhazia.
The Ossetians have traditionally had good relations with Russia, and North Ossetia is part of the Russian Federation.
Russia is hostile to Georgia's ambition to join Nato and has accused Georgia of building up its forces around the breakaway regions, where Russian peacekeeping troops are deployed.
BBC website readers have been giving their reaction to the current situation in the region:
Our government did everything not to answer shooting from separatists, but they continued even after Saakashvili's declaration. They were shooting for over 2 hour and our side was not responding.. I live in Gori, it is very near from Tskhinvali. I heard all the shooting. Even now I can hear some shooting. I'm praying everything will be OK. I hope our military army will kick out the criminals from our land. Mikheil Sukhitashvili, Gori, Georgia
The Georgian nation and Georgian refugees from its breakaway regions, have been waiting for 17 years to return to their homes, but Russian FSB trained breakaway region leaders of south Ossetia and Abkazia did nothing to bring peace in the region. I believe Georgia has full constitutional right to bring law and order on its world recognised sovereign territory. Otto, London
There are hundreds of "volunteers" infiltrating into the region from the Russian side. Russia does everything to stop Georgia form entering NATO and it is because of widespread ignorance of western Europe in recent years. That is what appeasement does. David, Tbilisi
We all Georgians are for peace, but sometimes it is getting difficult to get peace without the battle. War is something rational in the sense of its aims and goals, but the results might be destructive not only for Georgia, but for whole region. The democratic world should contribute in solving this problem. By the way, the neglect of this problem from Western countries propagated the processes. God is with us! lasha Chochua, Tbilisi
Unfortunately for international peace efforts in South Ossetia the recent Kosovo precedent has created conditions for South Ossetian independence and unilateral secession from Georgia. A independent South Ossetia is now both easily facilitated and there is no incentive for the South Ossetians to stay in union with Georgia. In edition there is no credible standing for Georgia to resist this under international law. Mihilo, Buffalo, Ny
I applaud Georgia's decisiveness to finally restore the order at home and get rid of Kokoity, this local self-proclaimed "tzar" whose ambitions only led to suffering of his own people. As a Ukrainian, I believe that now it is time for Kyiv to fulfil its strategic partnership with Tbilisi by announcing its readiness to help Georgia militarily if Abkhazia decides to open their so-called "second front". Ukraine's involvement, on the other hand, will help cool down many hot heads in Moscow who advocate that Moscow gets involved in Georgia's affairs on the basis that many South Osetians and Abkhazians have Russian passports. Dmitry Koublitsky, Detroit, USA
Georgia says: "I offer you an immediate ceasefire and the immediate beginning of talks"?!! Don't trust them!!! Army use heavy guns and MLRS "GRAD" against civilians: they are attacking Tskhinval right now. Words to you at the morning, swords to us at the night. Mikhail, Tskhinval, South Ossetia
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