(CNN) -- Syria's ambassador to Iraq, Nawaf al-Fares, has defected from the Syrian government, two members of the Syrian National Council opposition group told CNN on Wednesday.

Al-Fares would be the highest-ranking diplomat to defect since the uprising against President Bashar al-Assad's regime.

According to Dr. Hassan Chalabi, a Syrian National Council member, al-Fares is "currently making his way to a safe area."

Chalabi said he was working closely with his contacts in Iraq to coordinate with al-Fares to secure his safety. Another SNC member, Emad-eddin al-Rashid, told CNN that al-Fares is still in Iraq.

The Iraqi government has not commented on the news. It follows the apparent defection last week of a senior military figure, Brig. Gen. Manaf Tlas, in a protest of the killing of Sunnis.

Tlas, a Republican Guard military commander, is the son of a former defense minister and possibly the most senior Sunni in a power structure dominated by the Alawite minority.

Speaking at a "Friends of Syria" meeting in Paris last Friday, U.S. Secretary of State Hillary Clinton said there was an "increasing stream of military defectors" leaving Syria.

"Regime insiders and the military establishment are starting to vote with their feet," she said. "Those who have the closest knowledge of Assad's actions and crimes are moving away, and we think that's a very promising development. And it also raises questions for those who remain in Damascus."

Meanwhile, the violence in Syria continues, with at least 34 people killed across the country Wednesday, the opposition Local Coordination Committees of Syria said.

In another development, the head of the Syrian National Council is reportedly visiting Russia's foreign minister -- a notable meeting between a major Syrian opposition group and a government that some opposition members have accused of backing the Syrian regime.

SNC leader Abdul Basit Sieda said he would lay out a series of proposals on how to resolve the Syrian crisis during his meeting with Russian Foreign Minister Sergey Lavrov, Russia's official Itar-Tass news agency said Wednesday.

Shortly after Sieda came to the helm of the SNC last month, he called on officials in Syria, Russia and China "to think carefully about the situation now because the whole stability of the region, if not the whole stability of the world, is at stake here. We would like to call upon them to support the Syrian people."

Russia and China have vetoed U.N. Security Council draft resolutions that would have formally condemned the Syrian regime. Many other nations said such resolutions could have pushed al-Assad to stop a bloody, sustained crackdown on dissidents seeking his ouster.

Analysts say regime forces and rebel fighters are now locked in a deadly stalemate, with neither side willing to drop its weapons.

The Russians, long steadfast supporters of al-Assad and his father before him, have opposed international calls for him to be forced from power -- also a key demand of the Syrian opposition.

Wednesday's reported meeting comes amid an apparent shift in tone from Moscow, however.

Though it has been a longtime arms supplier to Syria, Russia said this week that it will not deliver new weapons to Syria as long as the situation there is unstable.

Former U.S. Ambassador to the Soviet Union Jack Matlock told CNN on Tuesday that Russia shared many of the U.S. concerns about the unrest in Syria, but is reluctant to embrace Washington's proposals to solve them because it is wary of its motives.

Meanwhile, international envoy Kofi Annan will brief the U.N. Security Council on Wednesday after a flurry of diplomatic efforts to end the 16 months of carnage, in which opposition groups say as many as 17,000 people have died. The United Nations has put the death toll at more than 10,000.

The briefing comes a week before the council must decide what to do with 300 U.N. observers whose work in Syria has been suspended because of the violence. Russia has tabled a draft resolution suggesting an extension of the United Nations' observer mission in Syria for another three months, Itar-Tass reported Wednesday.

Annan, the U.N.-Arab League special envoy to Syria, visited Iran and Iraq on Tuesday. He said he sees Iran as a factor in diplomatic efforts to forge peace in Syria.

The special envoy was visiting leaders in the region to find ways to implement his six-point peace plan for Syria, which includes a cessation of violence. Critics say the plan has failed, with dozens of Syrians reportedly killed every day.

But Annan said he believes Iran, a friend and ally of the al-Assad regime, can help end the violence.

"I think Iran can play a positive role," he said during a news conference with Iranian Foreign Minister Ali Akbar Salehi.

But the United States and other nations exploring peace moves in Syria have opposed Iranian participation in the diplomacy. U.S. State Department spokesman Patrick Ventrell cited "Iran's destructive behavior in Syria," a reference to its support of the government's fierce offensive against dissidents.

"If the Iranian regime wants to stop giving direct material support to the Syrian killing machine, then -- and play a constructive role -- we would welcome that," he told reporters Monday. "We're not at that point yet."

Also on Tuesday, Annan discussed Syria with Iraqi Prime Minister Nuri al-Maliki in Baghdad. As the conflict persists, Syrians are fleeing to neighboring countries such as Iraq.

Annan's visits to Iran and Iraq came after he met with al-Assad in Damascus on Monday. Annan said al-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 said the two discussed efforts to end violence, but he didn't want to mention details until he talked with opposition leaders.

World powers have condemned the al-Assad government's assaults against civilians.

But the diplomatic wranglings, such as Annan's recent Action Group meeting in Geneva and the U.S.- and Arab-backed Friends of Syria initiative, have failed to stop the killings of thousands since March 2011.

Meanwhile, two Russian military transport ships are en route Syrian port of Tartous, a U.S. official said.

Russia has said the visit is part of a training exercise.

But the ships have been closely watched by U.S. intelligence for the last several weeks while docked in the Black Sea port of Sevastopol. The Russians have said any weapons and personnel on board the ship are for reinforcement of the Tartous facility.

CNN's Amir Ahmed, Barbara Starr, Mitra Mobsherat and Karen Smith contributed to this report.