OSCE decisions require the consensus of all 55 members.
Western diplomats told RFE/RL they believe Russia has three major objectives.
First, Moscow wants to modify the OSCE's monitoring operations in the Chechen, Ingush, and Daghestani sectors of the Georgian-Russian border.
Second, Russia wants changes in the fees paid by the 55 members to finance the OSCE. The fees differ according to the economic strengths of individual countries.
And third, Moscow wants a reassessment of the OSCE's budget for 2005.
Richard Murphy, a spokesman for the OSCE, told RFE/RL that no solution to the standoff is in sight.
"No decision has yet been made on the future of the Georgia monitoring operation," Murphy said. "And further discussions will continue between now and the end of the year on this and a number of other issues, including the 2005 OSCE budget and the scale of contributions -- the amount of money that the OSCE participating states contribute to the budget every year."
All the changes being sought by Russia were raised by Foreign Minister Sergei Lavrov at a meeting of the OSCE's foreign ministers in Sofia in December. Lavrov repeatedly warned that Russia might block next year's budget unless the OSCE met at least some of its demands.
Russia particularly wants to stop the OSCE's monitoring operations on the mountainous Georgian-Russian border. Monitoring of the Chechen sector began in 1999 after Russia charged that armed Chechen fighters were crossing back and forth. It was extended in 2001 to the Ingush sector and in 2002 to the Daghestani sector.
The monitors are unarmed military officers drawn from about 30 countries, including Russia. In the summer, about 150 monitors are deployed in the mountains. That number sinks to around 70 in winter, when mountain passes are blocked by snow.
The monitoring is done on foot and by helicopter.
At this month's meeting in Sofia, U.S. Secretary of State Colin Powell said the operation should continue. He said it is contributing to stability on a "sensitive border" and recommended that its mandate be extended for another year.
Georgian Foreign Minister Salome Zourabishvili described the monitoring as "one of the most successful missions of our organization and one that makes a tremendous contribution to Georgia's security."
Lavrov told the Sofia conference that the monitoring operation has improved the situation on the border so much that it is no longer necessary. Lavrov also argued that Russian and Georgian border guards cooperate well and are able to protect the border without the OSCE's help.
Western diplomats who asked not to be identified said they hope a compromise can be worked out before the end of December that would allow the monitoring to continue, but possibly on a reduced scale.
They said it could be part of a package that might also contain compromise agreements on a revised scale of contributions to OSCE operations and on the budget for 2005.