Russian president Dmitri Medvedev has offered full support for the peace mission to Syria led by special envoy Kofi Annan.
Russia says it wants to avoid a long-lasting and bloody civil war in Syria.
Mr Annan, a former secretary-general of the United Nations, and the the UN-Arab League peace envoy, has been urged to work with the Syrian government and opposition to end the violence, the BBC reports.
The UN says the conflict has cost more than 8000 lives since it began in March last year. The Syrian government blames violence on "terrorist gangs" and says about 3000 members of the security forces have been killed.
Mr Annan has been trying to persuade Russia - a key ally of Syria - to take a firmer stance against President Bashar al-Assad.
He also used the meeting on Sunday to tell Syria that his mediation efforts were an opportunity, saying Damascus could put an end to the fighting and once again urged the Syrians to allow humanitarian aid into the worst-hit areas.
Kofi Annan will later go to China, which has also usually backed Syria at the UN.
More violence in Syria
Activists reported further bombardments and casualties on Sunday in the Homs area, killing at least five people.
Shelling was also reported in Hama, and tanks were seen in the streets of the southern town of Nawa, according to the Local Coordination Committees said.
More than 50 people were reported to have been killed in shelling or shooting by the security forces on Saturday, many of them in Homs.