Syrian opposition groups in exile, which enjoy Western support, have said they will not join the November 18 "Congress of Syrian National Dialogue" to be held in the Black Sea city and are aimed at ending the six-year war.
"We consider that the UN must be front and center," France's UN ambassador Francois Delattre told reporters.
"Any initiative that reinforces the Geneva process is welcome. Any initiative that would be outside the Geneva process is not, and is doomed to fail," he said.
During a meeting in the Kazakh capital of Astana this week, Russia and Iran, which back Assad, and Turkey, a key opposition supporter, agreed to hold the "congress" to bring the two sides together.
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"The road to peace lies through Geneva," Britain's UN ambassador Matthew Rycroft said.
"Now we are told that the road, which has already taken a significant detour into Astana, now needs another detour into Sochi. I'm relatively skeptical about that," he added.
Western powers have been wary of Russia's diplomatic initiatives on Syria, which they see as favoring Assad, although Paris and London have yet to agree with the new US administration on a common approach to ending the war.
Negotiations in Geneva have been deadlocked over Assad's fate, with the opposition demanding that any settlement provide for a transition away from his rule.
More than 330,000 people have died and millions have been driven from their homes in the conflict in Syria.