Annan spoke after holding talks in Tehran on Tuesday with Ali Akbar Salehi, the Iranian foreign minister.
"Iran can play a positive role," he said, adding he would continue to work with the Iranian leadership to resolve the crisis.
"There is a risk that the situation in Syrian gets out of hand and spreads to the region," Annan told a joint news conference with Salehi, who hailed Annan's "neutrality".
Before flying to Tehran, Annan said in Damascus on Monday he had agreed on a new approach with President Bashar al-Assad to stop the violence.
Last week, Annan acknowledged that international efforts to find a political solution for Syria had failed and called for a greater role for Iran, saying Tehran "should be part of the solution".
Activists say the violence in Syria has killed more than 17,000 people since the conflict began in March 2011.
Iran role contested
Salman Shaikh, director of the Brookings Doha Center and an analyst on regional politics, said: "Kofi thinks you can't have a political transition and solution without the Iranians on board, but this is still part of the understanding that Assad and the regime will be part of the solution - an idea many of us have given up on."
The US has rejected Iranian participation in international meetings on the crisis in Syria.
Annan, the joint envoy for Syria from the UN and the Arab League, presented a peace plan earlier this year, but it has never been followed.
Government forces and rebels have widely disregarded a ceasefire that was to begin in April, and spreading violence has kept nearly 300 UN observers monitoring the truce stuck in their hotels in Syria.
After a two-hour meeting with Assad on Monday, Annan said the men had agreed on an "approach'' to stop the violence, and that the diplomat would share it with the armed opposition.
"I also stressed the importance of moving ahead with a political dialogue which the president accepts," Annan said.