The council unanimously called on both sides to support "sustained stability" along the cease-fire line and in the Kodori Gorge.
The decision comes as relations between Tbilisi and Sukhumi remain at an impasse, with Abkhazia rejecting a recent peace proposal from Georgia and Russia signalling it intends to increase its presence in the breakaway region.
The mission, known as UNOMIG, was established in 1993 to monitor the cease-fire that ended the 13-month war between Georgia and its breakaway region of Abkhazia.
In the resolution, passed on April 15, the Security Council urged all parties to address each other's security concerns and to refrain from acts of violence or political provocation.
Zalmay Khalilzad, the U.S. ambassador to the UN, welcomed the extension of the UNOMIG mandate, and praised the government of Georgian President Mikheil Saakashvili for extending a peace proposal to Abkhazia in late March.
"Beyond this resolution, the U.S. strongly welcomes the new initiatives put forward by the Georgian president to advance a negotiated political resolution of the Abkhazia conflict," Khalilzad said. "We urge the de facto authorities in Abkhazia to seriously consider these initiatives as well as the previous offers for economic cooperation proposed in Geneva earlier this year."
The March proposal, which included an offer of "unlimited autonomy," was rejected by Sukhumi. Saakashvili has since ordered government officials to prepare a revised offer.
The resolution was co-sponsored by Russia and the United States, together with four other countries. However, that did not prevent Khalilzad from criticizing Russia's role in Abkhazia.
Moscow last month dropped trade restrictions against Sukhumi, and has announced plans to establish representative missions in both Abkhazia and Georgia's second breakaway region, South Ossetia. (The UN debate also came just hours before Russia announced it is planning to establish trade and other legal links with Abkhazia and South Ossetia, a move Georgia condemned as a breach of international law.)
Khalilzad said such moves "undercut" Russia's stated support for the principles of Georgian sovereignty and territorial integrity
"We believe this will raise new concerns about military transparency in the region and thereby set back the peace process," Khalilzad said. "We are deeply concerned by reports from Moscow that Russia is planning on establishing semi-official representative missions in Abkhazia and South Ossetia without the approval of the Georgian government."
Russia's UN ambassador, Vitaly Churkin, welcomed the UNOMIG extension and its continued support of Russia as a key facilitator in the peace process. But he also lashed out at Khalilzad for his criticism of Moscow, and suggested Washington's recognition of Kosovo independence was no different from Russia's support of Abkhazia and South Ossetia.
"It is surprising to hear those concerns coming from countries who have just hastily recognized illegal unilateral proclamations of independence in other places," Churkin said. "So, those who voice concerns about international legality should first of all be mindful of their own actions."
Churkin also blamed Tbilisi for exacerbating tensions in the breakaway region. "Unfortunately, the situation in the area of the conflict is giving rise to concern," he said, "and let me say in this regard that I do have to respond to the statement which has just been made by Ambassador Khalilzad because the concerns he has expressed are completely missing the real problem of the Georgia-Abkhazia conflict."
He went on to describe the "real problem" as "a continued and increased military presence of Georgia in the Upper Kodori Valley."
"Despite the recommendations of the [UN] secretary-general, there is a continuing presence of the so-called youth patriotic camp in the area of the conflict, just several hundred meters away from the separation line," Churkin said.
At a press conference following the Security Council session, Georgian Ambassador Irakli Alasania welcomed language in the new resolution that refuted Russia's account of Georgian interference in Kodori and provided for the return home of internally displaced persons (IDPs).
"We are very pleased that in the resolution we have a few new segments that appear there, one of which is that contrary to one of the Security Council members assessments, the situation in Upper Abkhazia, which is Upper Kodori region, was assessed as stable," Alasania said. "And the second and very important segment is that Paragraph 10 talks about the reasonable time frames that the sides, and especially the side that is respectively interested in that, should create a secure environment for the [IDPs] to return to their homes."
UNOMIG, whose military headquarters are based in Sukhumi, comprises an international staff of roughly 150 military observers and police officers. In addition to overseeing CIS peacekeepers based in the breakaway region, UNOMIG assists in the return of IDPs and in infrastructure projects.