In the two days since a small advance team of United Nations observers arrived to monitor a truce brokered by the UN-Arab League special envoy Kofi Annan, dozens of people have been killed by government forces.
Mr Lavrov said there were those who want Mr Annan's "plan to fail", without specifying where the threat was coming from.
"They are doing this by delivering arms to the Syrian opposition and stimulating the activity of rebels who continue to attack both government facilities and ... civilian facilities on a daily basis," he said.
Members of Syria's opposition voiced cautious optimism that Russia could be changing its tone about the 13-month uprising against the president Bashar Al Assad's regime. Russia has been one of the Syrian government's most vocal supporters and has remained critical of arming opposition groups. But it has also urged cooperation with Mr Annan's plan.
Haitham Manna, a member of the opposition National Coordination Body delegation visting Mosocw, said yesterday that Russia had indicated support for democratic change in Syria.
"The representatives of the Russian government aren't inclined to support the idea of preservation of the dictatorial regime. They are talking about the need for continuing democratic changes, and it's very important for us," he said.
"Russia has all the necessary levers to apply pressure on Assad's government and help Annan's mission."
The latest peace initiative is part of Mr Annan's six-point peace plan to halt the violence and pave the way for talks between the government and opposition.
A key provision of the plan - for troops and heavy weaponry to be withdrawn from population centres - appears to have been largely ignored.
The six-member UN observer team arrived on Sunday to monitor the ceasefire that came into effect last Thursday. So far there appears to have been only a moderate reduction violence.
At least 26 people were killed yesterday, including 19 in the northern province of Idlib, according to the Local Coordination Committees, a network of opposition activists. These figures could not be independently verified.
Activists said government troops fired mortars at two villages in Idlib yesterday. There were also reports of further shelling, including in Khalidiya and Bayada in the city of Homs, parts of which have been under attack since Saturday.
The UN secretary-general Ban Ki-moon, speaking in Luxembourg yesterday, said the fragile truce was being "generally observed". However, he said the eventual 250-person UN monitoring team may not be enough, "considering the current situation and the vastness of the country".
The UN is requesting helicopters and other aircraft from the European Union, he said, in order to ensure that the team has mobility during their mission. Mr Ban is expected to formally put the proposal to the Security Council today, but it is not clear if Mr Al Assad would agree to the plan or if his government would allow more observers into the country.
The US ambassador to the UN, Susan Rice, questioned the viability of the monitoring mission should the violence continue.
"Should the violence persist and the ceasefire, or cessation of violence more aptly, not hold, that ... will call into question the wisdom and the viability of sending in the full monitoring presence," she said.
The advance observer team, which has an operations office in a UN facility in Damascus, is led by the Moroccan Col Ahmed Himmiche.
A French diplomatic source said the country's foreign minister has invited the US secretary of state Hillary Clinton and other foreign diplomats to a meeting in Paris tomorrow aimed at keeping up the pressure on Mr Al Assad. The meeting will include other members of the Friends of Syria group, such as the foreign ministers of Qatar and Turkey.
The Hizbollah chief, Hassan Nasrallah, said yesterday in an interview on the Russian state RT television network, that his group had tried to encourage members of the opposition to talk to the regime to end the crisis.
The head of the Lebanese Shiite movement said his group had wanted to "encourage them and to facilitate the process of dialogue with the regime, but these parties rejected dialogue".
* With additional reporting by Reuters and the Associated Press