Damascus agrees but opposition says President Bashar Al Assad must quit first.
Russian effort to mediate in Syria
The Russians propose "informal contacts" in Moscow beween opposition groups and the Syrian government, without conditions.
The opposition yesterday dismissed the possibility while Bashar Al Assad remains president. "The resignation of Assad is the condition for any negotiation on the transition to a democratic government in Syria," said Burhan Ghalioun, head of the opposition Syrian National Council.
Nevertheless, the Russian foreign ministry said its offer had received a "positive response" from Syrian authorities.
"We are expecting that the opposition will also give their assent in the next days and put the interests of the Syrian people before any other ideas," the ministry said.
The secretary-general of the world's largest Muslim body, the Organisation of Islamic Cooperation, yesterday urged the international community to do more to protect civilians in Syria. Ekmeleddin Ihsanoglu called for a solution to ensure stability while avoiding foreign intervention.
"I renew my calls to the international community, especially the UN Security Council, to take up its responsibilities in protecting civilians and taking all measures to end bloodshed in Syria," he said. It was "impossible to remain silent" when dozens of civilians were being killed every day, he added.
The OIC supports the Arab League plan under which Mr Al Assad would stand down in favour of a unity government.
The 22-member league is seeking support for its plan at the United Nations. The group's secretary-general, Nabil Elaraby, is due to address the UN Security Council today. Hillary Clinton, the US secretary of state, and the French foreign minister Alain Juppe will be at the meeting.
Yesterday, Mrs Clinton said the Security Council must act to end Mr Assad's "violent and brutal attacks" on demonstrators.
But Russia, a main military supplier to Syria, has said it will use its veto against a draft Security Council resolution, because it disapproves of language against arms deliveries.
Russia's deputy foreign minister Gennady Gatilov said Moscow believes the recommendations of an Arab observer mission - which suspended its work last week - should first be considered by the Council.
"It would be logical, considering the complexity of this issue, for Security Council members to be able to study the recommendations and conclusions of the observer mission in detail," he said.
"Only after that would it be possible to count on a substantive discussion of this issue in the Security Council."
Meanwhile, fierce clashes between the Syrian army and rebel forces continued yesterday just outside Damascus. Government troops fought to wrest control of neighbourhoods around the east of the capital taken by rebel soldiers last week.
The Free Syrian Army - made up primarily of defected soldiers - was forced to retreat from some areas, according to activists, but continued attacks on government troops.
"Street fighting has been raging since dawn," said one opposition activist in the suburb of Saqba. "The sound of gunfire is everywhere."
The three days of intense fighting just outside Damascus have left several dozen people dead, according to activists.
The Local Coordination Committees (LCC), a network of opposition activists, said at least 40 people were killed yesterday, including six children. Most were killed in violence in Homs, the Damascus suburbs and in Daraa - the town where protests against the Al Assad regime started more than 10 months ago.
The LCC said a couple and their four children were among the dead in Homs.
The Syrian state news agency, Sana, reported yesterday that an "armed terrorist group" blew up a gas-pipeline near the town of Tal Kalakh, close to the border with Lebanon. The agency also reported that funerals were held yesterday for another 22 security force members killed in Homs, Idleb and outside Damascus.
As pressure on the Syrian government mounts at home and abroad, Iran has said Syria should be given more time to implement promised political reforms.
Arab foreign ministers are due to meet next on Sunday to decide their next step in efforts to end the 10 months of violence that have killed more than 5,400 people, according to a UN estimate this month.
The Syrian government said in December that 2,000 members of its security forces have been killed by what it has described as terrorist groups.
* With additional reports by Agence France-Presse, Reuters and the Associated Press