Lavrov also repeatedly accused other nations of egging the rebels on and pushing them to break the ceasefire and provoke a response from Assad's forces, in the hope of forcing international intervention.
"All the parties involved need to be playing the same tune," Lavrov said.
"We should be attempting to implement the peace plan and not trying to change the regime. It's time to choose between pursuing geopolitical goals and saving lives."
As Annan arrived in Syria - a country still coming to terms with the deaths of 108 people including dozens of women and children in Houla - there were reports of escalating fighting in the central city of Hama, where the opposition says Syrian army artillery barrages have killed 41 people.
"I am personally shocked and horrified by the tragic incident in Houla ... which took so many innocent lives, children, women and men," Annan said before entering talks with Assad and other senior officials. The UN's peace envoy said all sides had to end the bloodshed, insisting that "this message of peace is not only for the Government, but for everyone with a gun".
The Syrian Government continues to blame the Houla massacre on "terrorists" and Sunni fundamentalists, but has not spelled out in convincing detail how it believes the mass killings occurred.
Anti-government opposition sources in Damascus said they had been told by surviving villagers at Houla that, after fighting between the Free Syrian Army and regular government forces last Friday, Alawite militiamen entered the village and began the massacre.
They said the militiamen were acting in retaliation for the killing of a government informant in their village a month ago, but this could not be independently confirmed.
The mood in Damascus is becoming increasingly tense as people absorb the shock of the atrocity at Houla.
There is the sound of sporadic shooting in parts of the capital and the explosion of a bomb near a school in one suburb sent parents racing to pick up their children. Government control is tight in the centre of the city and there are many more checkpoints late at night. Independent