In his latest report on Abkhazia, UN Secretary-General Ban Ki-moon noted a "resurgence of tensions" between Georgia and its breakaway republic in the last four months, and called on the sides to preserve the integrity of the current ceasefire, signed in 1994 in Moscow.
A series of explosions rocked cities in Abkhazia in late June and early July, killing four people, including a staff member of the UN Observer Mission in Georgia, and wounding 18.
"I am deeply concerned by this resort to indiscriminate violence, an unprecedented development with unpredictable consequences for a fragile peace process," Ban said.
At the meeting on Tuesday, Ban intends to report to the Security Council on the results of an assessment of the peace process, which "will explore the possibility of a coordinated international response to avert further worsening of the political and security situation."
Russia is again expected to call for an agreement on the non-use of force between Georgia and Abkhazia, amid rising tensions and fears of military conflict in the region.
Abkhazia rejected a German peace plan, backed by the EU, on July 18. The plan stipulated a non-violence agreement, confidence-building measures over the next year to lead to a determination of Abkhazia's status, and the return of Georgian refugees.
"We are not going to discuss Abkhazia's status," Bagapsh said. "Abkhazia is an independent state."
Bagapsh also said that the return of Georgian refugees to Abkhazia could only start only after the withdrawal of Georgian troops from the Kodori Gorge and the signing of a non-aggression pact.
Some 300,000 Georgians fled Abkhazia in 1991-93 amid accusations of ethnic cleansing. On May 15 this year, the UN General Assembly adopted a resolution acknowledging ethnic cleansing in Abkhazia and called for the return of Georgian refugees.
Abkhazia, alongside South Ossetia, another Georgian breakaway republic, announced independence from Georgia in the early 1990s following the collapse of the Soviet Union. Between 10,000 and 30,000 people were killed in the ensuing Georgian-Abkhazian conflict.
Relations between Russia and Georgia have deteriorated in recent years over Moscow's support for the rebel provinces, and Tbilisi's drive for NATO membership.
Georgia has accused Russia of fueling tensions in the region with the aim of annexing the republics. Moscow has rejected the accusations, claiming that Tbilisi is planning to invade both Abkhazia and South Ossetia. Both countries have accused each other of troop build-ups in the area.
Last Tuesday, the UN Security Council held a closed session at Georgia's request to discuss an incursion into Georgian airspace by Russian military aircraft.
Georgia requested the session on July 10 in response to an admission by Russia on the same day that its fighters had flown over South Ossetia two days earlier.
Russia said it had carried out the flights over fears that Georgia could invade the de facto independent republic. Tbilisi called the flights an act of "military aggression," and recalled its ambassador from Moscow.