"Others say it is impossible to let him leave. Not only would it let him get away with thousands of murders and the destruction of the country, but it also would give him a green light to keep on doing what's he's doing, knowing that when he decides to leave, he can leave."

But Allaf said she thinks there is "absolutely zero" chance that the president will take up the Arab League's offer.

"I think Assad does not plan on ever accepting any possible plans for escaping or leaving," she said. "I think he will keep on fighting, hoping the revolution will stop."

The Syrian government has long maintained that "armed terrorist groups" are fueling violence in the country.

Responding to a question about clashes in Damascus, Makdissi said, "We are in a state of self-defense."

But he later added, "This is an exceptional matter. It will last a couple of days, and matters will return to normal."

On Monday, chaos ensued in cities across the country, opposition activists said.

In Homs, two people were killed "due to intense shelling by helicopters and rocket launchers, accompanied by intense clashes between the (rebel) Free Syrian Army and the regime army," the LCC said.

The LCC reported fierce clashes for a second day in Aleppo, Syria's largest city and commercial hub. In a video posted online Sunday, the head of the rebel Free Syrian Army in Aleppo announced an operation "to liberate the city of Aleppo from the rule of the Assad thugs, whose hands were blood-stained by heinous crimes against our people."

Brig. Gen. Abdel Jabbar Al-Obeidi also vowed to secure Aleppo and protect all minorities and sects, including the members of Alawite sect that the president belongs to.

If rebels eventually gain control of Aleppo, it would mark a pivotal point in the Syrian crisis and deal a heavy blow to al-Assad's financial ties.

The Syrian crisis started in March 2011, when a fierce government crackdown against protesters morphed into a nationwide uprising against the regime.

The United Nations estimates more than 10,000 people have been killed since the crisis began more than 16 months ago. But Rupert Colville, a spokesman for the office of the U.N. high commissioner for human rights, said the United Nations has not been giving out overall death toll numbers since December "because it became impossible to verify the numbers in any meaningful way."

Opposition groups tracking deaths have issued higher tolls. The LCC, for example, estimates more than 16,000 people -- mostly civilians -- have died.

In addition to the deaths, thousands of refugees have fled Syria into neighboring countries to escape the turmoil.

The three border crossings between Iraq and Syria were opened Monday to Syrian refugees, an Iraqi government spokesman said.

"The border guards, police and border provinces were guided to provide all the needed support to the Syrian refugees," Ali al-Dabbagh said in a written statement.

The United States will give Jordan $100 million in special economic aid to help ease the burden of hosting Syrian refugees, the U.S. Embassy in Jordan said Monday.