Русская версияRussian-backed rebels in Abkhazia say they have begun an operation against Georgian forces, as UN moves to achieve a ceasefire failed to make progress.
The rebels say they are trying to push Georgian forces from a strategic gorge in the west of the breakaway province.
France's president is visiting Russia and Georgia on Tuesday but a new French draft resolution at the UN has already drawn strong Russian criticism.
The US president has meanwhile strongly attacked the Russian "invasion".
George W Bush said the Russian actions in Abkhazia and the other breakaway province of South Ossetia were "unacceptable in the 21st Century" and that Moscow was guilty of a "dramatic and brutal escalation".
Bloody fighting
The Russian-backed separatists' government in Abkhazia said its forces aimed to "squeeze" Georgian troops out of the upper part of the Kodori Gorge.
Click to view a map of the region
They launched their attack at 0600 local time (0200 GMT) and Russian TV has reported heavy gunfire and air strikes by what it says are Abkhaz planes.
There was no immediate confirmation of the offensive from the Georgian government.
Abkhazia, a much bigger province than South Ossetia, also broke away from Georgia during the collapse of the USSR in the early 1990s.
Russian troops who arrived there in recent days launched raids into Georgia proper on Monday, destroying a military base in the town of Senaki and taking control of another town, Zugdidi.
Georgia has been withdrawing its troops and armour towards Tbilisi after four days of bloody fighting in South Ossetia with Russian troops and rebel fighters.
The Red Cross has said it is still too early to say how many people have been killed or injured by the fighting, which has created thousands of refugees on both sides.
Surprise attack
French President Nicolas Sarkozy, whose country currently chairs the EU, is to meet Russian President Dmitry Medvedev in Moscow before travelling to Georgia for talks with its president, Mikhail Saakashvili.
However, Russia's envoy to the UN, Vitaly Churkin, has already dismissed a three-point French peace plan put to the Security Council in a draft resolution.
Ambassador Churkin said the plan contained "no reference to Georgian aggression or Georgian atrocities".
Moscow has called for an emergency meeting with Nato to discuss the conflict, which erupted after the Georgians launched a surprise attack on Thursday night to retake South Ossetia and Russia sent in its forces to eject them.
In his comments on Monday, President Bush strongly criticised Russia, suggesting it might be planning to depose the Georgian government.
"Russia's government must respect Georgia's territorial integrity and sovereignty," he said.
"The Russian government must reverse the course it appears to be on."
But Mr Bush stopped short of specifying any consequences if Russia failed to heed Western appeals for an end to the fighting.
European rhetoric
Whatever the unease in many Western capitals at the rash thinking that led President Saakashvili to order his troops into South Ossetia, there is growing outrage, BBC diplomatic correspondent Jonathan Marcus reports.
Many believe that Moscow has gone too far, he says.
By moving beyond the territory of the separatist enclaves, Russia's forces are close to cutting key transport links between Tbilisi and Georgia's Black sea ports, raising concerns about its wider strategic goals.
President Sarkozy's diplomatic round on Tuesday is a tangible signal of European concern, our correspondent says.
In Moscow, he may have uncompromising words for President Dmitry Medvedev but in Tbilisi he is likely to be hailed in much the same way as former French President Francois Mitterrand was feted when he visited Sarajevo during the dark days of the siege in 1992, he adds.
But the harsh truth is that the West has relatively few diplomatic cards to play against a powerful neighbour which controls much of Europe's energy supplies, he says.
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(BBC)
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