Russia has put its military bases on high alert in the South Caucasus country and withdrawn most of its diplomats, since Georgian authorities arrested Russian officers they accused of spying last week.
OSCE Chairman-in-Office, Belgian Foreign Minister Karel De Gucht, said: "I appeal to all concerned parties to abide by the principles of international law, to abstain from provocations, to establish direct dialogue and to find a quick solution."
"I will remain in contact with all the relevant parties and work towards this end," the minister said, adding that he is ready to travel to the region if his presence could help bring about a breakthrough.
On Thursday in Vienna, the OSCE chairman had urged political leaders to "show vision and take responsibility to help solve 'frozen conflicts', such as those in South Ossetia and Abkhazia, that threaten to erupt anew at any time," the OSCE statement said.
The commander of Russian troops in the South Caucasus said earlier that troops at Russia's Akhalkalaki and Batumi military bases in Georgia have been ordered to 'shoot to kill' if provoked.
The latest diplomatic clash between the countries has served to further aggravate relations, which have been volatile over the past few years due partly to Russia's involvement in Georgia's breakaway republics of Abkhazia and South Ossetia, where Russian peacekeeping forces have been stationed since bloody conflicts that took place in the early 1990s.