Georgia acknowledges that one pilotless reconnaissance plane was shot down over Abkhazia last month. But it contends that the drone was taken out by a Russian warplane, not Abkhaz forces.
Since then, Abkhazia has claimed to have shot down at least five other such planes.
The claims come amid a sharp escalation of tension over the region, which has had de facto independence from Georgia since the end of a mid-1990s separatist war. NATO has said it will eventually grant membership to Georgia, a country that Russia sees as part of its historical sphere of influence.
Abkhazia alleges that Georgia is preparing to try to retake the region by force. It claims that there has been a significant increase in Georgian forces in the upper Kodor Gorge region, the only section of Abkhazia under Georgian control.
In response to Abkhazia's claims of Georgian aggression, Russia has increased its contingent of peacekeeping troops in Abkhazia.
Georgian officials interpret that increase as veiled aggression, saying the peacekeepers support Abkhazia's separatists.
On Monday, Abkhazia's separatist foreign minister, Sergei Shamba, said a pilotless drone was shot down over the Gali district, near the southern administrative border with Georgia, in the afternoon. About an hour later, the presidential envoy to the district, Ruslan Kishmaria, said a second plane had been downed.
Georgian Interior Ministry spokesman Shota Utiashvili denied both claims.
Russia does not formally recognize the government of Abkhazia, but it has granted Russian passports to most of the territory's residents. It called last month for closer ties with Abkhazia and South Ossetia.
The tensions have sparked concern in the West, which wants to integrate Georgia with Europe but also seeks to improve relations with Russia.
The foreign ministers of five EU countries -- Poland, Slovenia, Lithuania, Latvia and Sweden -- also visited Georgia on Monday. They met Georgian President Mikheil Saakashvili as well as Foreign Minister Ekaterine Tkeshelashvili. "The European Union reiterates its firm commitment to the sovereignty, independence and territorial integrity of Georgia within its internationally recognized borders," Dmitrij Rupel, Slovenian foreign minister, told a news conference.
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