UN and Arab League peace envoy Kofi Annan will brief the UN Security Council on Wednesday on the Syria crisis after a tour through Damascus, Tehran and Baghdad, he told journalists in Iraq.

Speaking on Tuesday in Baghdad, Annan also warned of "serious pockets" of violence close to Syria's border with Iraq, adding that Iraqi Prime Minister Nuri al-Maliki was concerned by the unrest and supported his peace plan.

Annan's surprise visit to Iraq was his first to the country since becoming the UN-Arab League envoy to Syria.

"I leave tonight and tomorrow, I'll be briefing the security council," Annan told journalists in Baghdad in a short briefing in the heavily fortified Green Zone, after meeting Maliki.

"And I'm sure the council will take appropriate action, including the future of UNSMIS, the monitors on the ground, as their mandate comes up on the 21st of July."

The 300-strong UN Supervision Mission in Syria (UNSMIS) was suspended in mid-June because of intense violence across the country.

The unarmed observers were deployed as part of Annan's six-point plan to end the Syria conflict, which included a ceasefire that has been violated daily since it took effect on April 12.

Annan added that he had "very good discussions with Prime Minister Maliki who, like all of us, is extremely concerned about the killing and supports the six-point plan and its comprehensive implementation."

"There are serious pockets of violence around Iraq," warned the former UN chief and spoke of the "need of being creative in stopping the violence."

"We've tried it at the national level on the 12th of April and it didn't hold," he said, adding that parties should now focus on trying to "build it from the ground up rather than the other way round."

Earlier on Tuesday, Iran reiterated its full support for Annan's peace plan, saying it should be fully implemented to restore stability.

"We expect that Mr Annan will continue his efforts to bring about stability and peace in Syria and the region," Foreign Minister Ali Akbar Salehi said at a joint news conference in Tehran with Annan.

The envoy visited Iran after talks with embattled Syrian President Bashar al-Assad on Monday and following an international meeting in Geneva last month to which Iran, Damascus's staunchest regional ally, was not invited.

Annan said he agreed with Assad on a new political "approach" to end the nearly 16-month conflict that he would put to the rebels. He would not elaborate, saying he must first talk to the Syrian opposition.

Tehran was excluded from the Geneva talks -- which the Islamic republic dubbed "unsuccessful" -- following US and EU objections.

The gathering in Switzerland agreed a plan for a political transition in Syria which did not make an explicit call for Assad to quit, although the West and the opposition made clear it saw no role for him in a unity government.

Monitors say that more than 17,000 people have been killed in Syria since mid-March 2011.