At the meeting, the sides are discussing means of ending the current crisis in the Kodori Gorge, the boundary between Georgia and Abkhazia.
Georgian media reported earlier in the day that a military column was traveling to the gorge.
Rustavi-2 TV channel said Emzar Kvitsiani, former President Eduard Shevardnadze's envoy to the Kodori Gorge, was himself meeting with the elders of the district in Svaneti, near the Kodori Gorge.
As the news of Georgia's military column broke out some officials in other countries expressed concerns that Georgia was initiating a war on Abkhazia.
But the Georgian foreign minister issued a pointblank denial Tuesday that Tbilisi might conduct a military operation in the Kodori Gorge.
"We categorically rule out a military operation in the Kodori Gorge or anywhere in de-facto Abkhazia," Gela Bezhuashvili said.
Bezhuashvili said that the Georgian authorities would not put up with "anarchy and arbitrariness" but added that, "Only police forces will be used to establish order."
The Russian Foreign Ministry said earlier on Tuesday that Moscow was keeping a close eye on the situation in the Kodori Gorge, and urged the Georgian side to refrain from the use of force that could provoke a new conflict in the region.
Russia assisted in concluding ceasefire agreements between Georgia and its separatist republics Abkhazia and South Ossetia in the early 1990s, and Russian peacekeepers have since helped maintain ceasefire in the conflict zones.
