BAGHDAD — The U.N.’s special envoy on the Syrian crisis sought to build support for his peace efforts Tuesday with the leaders of Iran and Iraq, saying President Bashar Assad has agreed to a plan to quell the bloodshed in the most violent areas of Syria and then expand the operation to the whole country.

Top diplomat Kofi Annan said at a news conference in Iran that the plan still must be presented to the Syrian opposition. But he said his talks with Assad a day earlier focused on a new approach to 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 Tehran, his first step on a tour of Syria’s allies. He did not elaborate on the plan.

Annan later visited Iraq and met Prime Minister Nouri al-Maliki to discuss ways to end the fighting.

“I think we’ve all watched the tragic situation in Syria, the killings, the suffering of the people,” Annan said in Baghdad. “And everyone I’ve spoken to shares the concerns and the needs for us to stop the killing.”

The conflict in Syria has defied every international attempt to bring peace, and there was no sign that the plan Annan described Tuesday will be a breakthrough. Although the Assad government’s crackdown has turned the Syrian president into an international pariah, he still has the support of strong allies such as Russia, Iran and China.

There is little support for military intervention of the type that helped bring down Libya’s Moammar Gadhafi, and several rounds of sanctions and other attempts to isolate Assad have done little to stop the bloodshed.

Still, Annan’s latest efforts to reach out to Syrian allies suggest he sees them as integral to solving the crisis.

Annan was scheduled to brief a closed meeting of the U.N. Security Council by videoconference from Geneva on Wednesday on his meeting with Assad and visits to Iran and Iraq.

The council must decide in the coming days whether to extend the mandate of the U.N. observer force in Syria, which expires on July 20.

In New York, a U.N. diplomat, speaking on condition of anonymity because he was not authorized to speak publicly, said that Russia has circulated a draft resolution to the U.N. Security Council that would extend the U.N. observer force in Syria but refocus its activities on trying to achieve a political solution to the conflict.

Since Assad took power following the death of his father, Hafez, in 2000, he has deepened cultural, political and economic ties with Iran, making it Syria’s strongest regional ally. Tehran, in turn, has boosted Assad’s military, providing it with advanced communications technology and weapons.

All of this makes Iran unlikely to support change in Syria.

On Tuesday, Annan said Tehran has offered its support to end the conflict and must be “part of the solution.”

“My presence here proves that I believe Iran can play a positive role and should therefore be a part of the solution in the Syrian crisis,” Annan told reporters in Tehran after meeting with Iranian Foreign Minister Ali Akbar Salehi.

Annan said he has “received encouragement and cooperation” from the Iranian government but did not elaborate. Salehi also did not spell out what Tehran was willing to do to help tame the violence.

Annan’s gestures to Iran in particular appear to oppose the approach of Washington, which has rejected Iran’s participation in helping solve the crisis.

State Department spokesman Patrick Ventrell said the U.S. doubts Iran will be able to play a constructive role.

“If the Iranian regime wants to stop giving direct material support to the Syrian killing machine ... we would welcome that.  We’re not at that point yet,” he said Monday.

Some have said Annan’s tour of Syria’s allies smacked of betrayal.

Rajeh Khoury, a columnist in Lebanon’s leading An-Nahar newspaper, wrote that Annan’s actions “give the Syrian regime more time to accomplish the impossible task of crushing the uprising militarily.”

“His insistence on making Iran part of the solution at a time the opposition sees Iran as part of the problem is extremely dangerous,” Khoury said.

The conflict in Syria is complicated by sectarian tensions. Sunnis make up most of Syria’s 22 million people, as well as the backbone of the opposition. But Assad and the ruling elite belong to the tiny Alawite sect, an offshoot of Shiite Islam.

Iraq’s prime minister is a Shiite, and Iran is a Shiite powerhouse in the region.

The six-point peace plan Annan brokered earlier this year has failed to gain traction on the ground in Syria.

Government forces and rebels have widely disregarded a cease-fire that was to begin in April, and spreading violence has kept nearly 300 U.N. observers monitoring the truce stuck in their hotels in Syria.

Annan stressed the urgency of finding a solution to the crisis.

“If we don’t make a real effort to resolve this issue peacefully and it were to get out of hand and spread in the region, it can lead to consequences that none of us could imagine,” he said.

Salehi said Tehran backs the rights of the Syrian people but opposes military intervention. He also blamed the conflict’s increasingly chaotic violence on the meddling of foreign powers.

“Unfortunately, the unwise interference of others has caused the situation in Syria to remain critical,” he said. “The worsening of the situation should not happen. It would not benefit anyone in the region.”

In other diplomatic efforts, an announcement posted on the Facebook page of the opposition Syrian National Council said a high-level delegation from the group, led by its head, Abdelbaset Sieda, was traveling to Moscow to discuss the situation in Syria with Russian officials. It gave no further details.

The International Committee of the Red Cross said one of its Syrian staff was shot and killed Tuesday while riding in a clearly marked ambulance in eastern Syria. It did not say who shot him.

The group said it was second time in a month that one of its workers had been killed and called on all sides to protect medics.

The Syrian conflict also has spilled outside the border several times. On Tuesday, the Lebanese army said shells were fired into Lebanon from Syria during an overnight exchange of fire along the countries’ frontier.

The Red Cross and Lebanon’s national news agency said a Lebanese and two Syrians died — one from a heart attack and two others when their motorcycle hit a car in the Wadi Khaled area, where the clashes took place.

The Lebanese government decided at a Cabinet meeting Monday night to boost the army’s presence along the volatile border, where shells fired from Syria have killed and wounded several Lebanese in the past few weeks.

Syria says the frontier is being used for smuggling weapons to rebels.

Also Tuesday, Jordan opened a new refugee camp near the border with Syria to handle the growing number of people fleeing the deadly violence.

The U.N. refugee agency had appealed to Jordan to accommodate the increased flow across the frontier, but the government in Amman has been reluctant to set up refugee camps, possibly to avoid angering Assad’s regime.

The new camp in the northern border town of Ramtha had to be set up because Syrian refugees could no longer be absorbed into border communities, said Jordanian Information Minister Sameeh Maaytah.

Since the uprising began, Jordan has sheltered 140,000 Syrian refugees. Lebanon hosts about 30,000 Syrians and Turkey has taken in tens of thousands of others.

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Dareini reported from Tehran, Iran. Associated Press writers Sinan Salaheddin in Baghdad, Zeina Karam in Beirut, Edith M. Lederer at the U.N., Dale Gavlak in Mafraq, Jordan, and Jamal Halaby in Amman, Jordan, and Edith M. Lederer at the United Nations contributed to this report.