The UN Security Council has unanimously adopted a resolution urging Georgia to refrain from provocative action in the breakaway region of Abkhazia.
Georgian troops entered the Kodori Gorge in July
The resolution also renewed the mandate of a UN mission in Abkhazia which began after the region split in the 1990s.
Tensions rose in July when Georgian troops entered Abkhazia's remote Kodori Gorge to drive out a rebel militia.
Russia had urged a stronger resolution to criticise Georgia for its presence in the Kodori Gorge.
The Georgian government has been consolidating its position in the upper part of the Kodori Gorge, the only area of Abkhazia which it controls, says the BBC's Matthew Collin in Tbilisi, Georgia's capital.
The separatists have raised fears that it could be used as a base for invasion, our correspondent says.
After taking control of the gorge in July, Tbilisi announced plans to set up a headquarters for Abkhazia's "legitimate government" there.
Russia has condemned the Georgian deployment in the gorge as a "serious violation of the 1994 Moscow ceasefire agreement", which halted fighting between Georgian and Abkhaz separatist forces.
The unrecognised Abkhaz government also protested against the Georgian move into the gorge.
Tbilisi has accused Russian troops in the breakaway regions of supporting the separatists in order to undermine President Mikhail Saakashvili's pro-Western government.
Georgia has demanded that Russia withdraw its troops from Abkhazia and another breakaway region - South Ossetia.
Moscow insists that its troops are peacekeepers, needed to prevent a resumption of hostilities.
Relations between Georgia and Russia worsened last month when Georgia briefly arrested four Russian officers on spying charges.
Moscow then expelled 132 Georgians living in Russia for immigration offences and imposed sanctions on Georgia.