At a news conference in Iran, Annan said the plan still must be presented to the opposition. But he said Assad suggested trying to calm specific areas a day earlier during talks in the Syrian capital aimed at ending the violence, which activists say has killed more than 17,000 people since March 2011.
“(Assad) made a suggestion of building an approach from the ground up in some of the districts where we have extreme violence to try and contain the violence in those districts and, step by step, build up and end the violence across the country,” Annan told reporters in Iran, his first step on a tour of Syria's staunchest allies.
Annan later visited Iraq and met Prime Minister Nouri al-Maliki to discuss ways to end the 16 months of bloodshed.
The conflict in Syria has defied every international attempt to bring peace, including an earlier effort by Annan, and there was no sign that the plan the UN-Arab envoy described today will be a breakthrough.
Although the government's crackdown has made Assad an international pariah, he still has the support of strong allies such as Russia, Iran and China.
The international community has little appetite for military intervention of the type that helped bring down Libya's Muammar Gaddafi last year, and several rounds of sanctions and other attempts to isolate Assad have done little to stop the bloodshed.
Annan's latest efforts to reach out to Syrian allies suggest he sees Assad's allies as integral to solving the crisis. Annan's outreach to Iran in particular appeared to oppose the approach of Washington, which has rejected Iran's participation in helping solve the crisis.