"A meeting with President Mikheil Saakashvili should be a result of resumed talks based on Georgia's unconditioned fulfillment of its obligations under previous agreements," Sergei Bagapsh and Eduard Kokoity said in a statement.
They said Georgia should withdraw its troops from the Kodori Gorge, the only Tbilisi-controlled area in Abkhazia, as well as from the Georgian-South Ossetian conflict zone, and cease all activities that destabilize the situation.
On Monday, Georgian President Mikheil Saakashvili proposed direct talks between Tbilisi and Tskhinvali, the capital of South Ossetia. Kokoity rejected the proposal the next day, saying the recent intrusion onto South Ossetian territory by armed Georgian militants made talks impossible.
On Monday, South Ossetian authorities said a group of four heavily armed terrorists was spotted in the breakaway region's Dzhava district, having infiltrated from Georgia. They opened fire on police during an identification check and were killed in the ensuing firefight. Georgian authorities denied any knowledge of the group.
South Ossetia and Abkhazia declared independence from Georgia following the collapse of the Soviet Union in 1991, unleashing bloody conflicts in the region. Russia mediated ceasefire agreements between the sides and Russian peacekeepers have been deployed in the conflict zones ever since.
Bagapsh and Kokoity praised a statement the Georgian foreign minister, Gela Bezhuashvili, made Tuesday, that "Russia should be one of the positive players in the resolution of the conflicts."
The leaders also said in the statement that Georgia was unilaterally revising and violating obligations it had assumed, and was ignoring recommendation from the UN Security Council.
"In this regard, any bilateral agreements lose all their meaning," the statement said. "The conflicts can be resolved and tensions in the region eased only through negotiations."
President Saakashvili, who came to power on the back of the 2003 "Rose Revolution," pledged to bring the self-proclaimed republics back into the fold. His defense minister also said Georgian troops would celebrate New Year's day in the capital of South Ossetia, Tskhinvali.
Georgia deployed massive troops in the Kodori Gorge, controlled by Abkhazia in its lower section, last summer under the guise of a police operation there. Russia called it a provocation and demanded their withdrawal.
On October 13, the UN Security Council unanimously approved a Russian-sponsored draft resolution on Georgia, urging the ex-Soviet country to refrain from provocative actions in Abkhazia and calling for an extension of the Russian peacekeeping mission in the region until April 15, 2007.
