Bassma Kodmani, a member of the opposition Syrian National Council, addressed reporters in Moscow following talks with Russian officials.
She said Syrian opposition groups want the United Nations to serve as the mediator for political transition in Damascus that would take place once the violence ends, Russia's state-run news service RIA Novosti reports.
Kodmani said she was opposed to direct negotiations with the government of Syrian President Bashar Assad, however.
Conflict in Syria passed the 16-month mark in July. More than 10,000 people are estimated to have died as a result of the ongoing violence. The Syrian government is accused of committing war crimes, though Damascus maintains it is dealing with domestic terrorism.
Russia has opposed to direct action at the U.N. Security Council, saying it's up to the Syrians to find a resolution to the crisis.
"We are definitely addressing Russia, which is one of the fundamental countries for Syria and plays a big role for us, with the hope that it will help us to turn the page of the old regime and transform to the new democratic order," Kodmani was quoted as saying.