Lavrov conceded that a rare speech Assad delivered on January 6 laying out his own vision for a peace settlement probably did not go far anough and would not appease the armed opposition.
But he also urged Assad's enemies to come out with a counterproposal that could get serious peace talks started between the two sides for the first time.
"President Assad has forwarded initiatives aimed at inviting all in the opposition to dialogue. Yes, this initiative probably does not go far enough," said Lavrov.
"They will probably not look serious to some. But these are offers. And if I were in the opposition's place, I would present my counter-ideas about establishing dialogue."
Russia on Saturday reiterated its support for a transition plan that was agreed in Geneva on June 30 but never implemented because of the fighting.
The accord is now being heavily promoted by UN-Arab League envoy on the 21-month crisis Lakhdar Brahimi.
The Geneva deal calls for power to be handed to an interim government but offers no clear guidance about Assad's future role.
Russia argues that only the Syrian people themselves can oust Assad through either elections or some form of negotiated settlement.
Western powers and Arab states -- as well as the armed opposition -- counter that the plan can only work if Assad steps down.