At least 66 people were killed Thursday as Syria's regime pounded a rebel stronghold with air strikes after a barrage of opposition fire hit the capital Damascus, a monitor said.

The Syrian Observatory for Human Rights said 12 children were among those killed in the opposition-held Eastern Ghouta region outside Damascus, and an AFP photographer there described chaotic scenes.

In the capital, meanwhile, a barrage of at least 120 rockets and mortar rounds fired by rebel forces killed 10 people, among them a child.

The fire left usually busy streets of the city deserted and prompted Damascus University to close for the day, sending students home.

The assault on the capital began early on Thursday and came two days after the leader of rebel group Jaysh al-Islam (Army of Islam) warned it would attack in response to repeated government strikes on rebel-held Douma in Eastern Ghouta.

"Within minutes, our busy street was empty," a resident of Damascus' Baramkeh neighbourhood told AFP after the mortar fire began, adding that the head teacher of a local school had been forced to take her students to a shelter.

The middle class district of the capital is home to several university buildings, as well as the headquarters of state news agency SANA.

In the city centre, traffic was light and many people stayed home from work.

"If the terrorists think that by shelling Damascus they will ease the pressure on them, they are making a big mistake," a senior military official said, speaking on condition of anonymity.

"We will continue to hunt them down and destroy them."

Jaysh al-Islam leader Zahran Alloush had warned that Damascus would be considered a "military zone" during the bombardment, which follows a similar attack by the group on January 25 that killed six.

The government's response was swift and deadly, with more than 60 air strikes hitting areas across Eastern Ghouta, along with surface-to-surface missiles, the Observatory said.

AFP photographer Abd Doumany said the assault caused chaos.

"This is the worst day in Douma in four years," he said.

"The situation in the hospitals is very bad. There are shortages of everything."

He said medics had been wounded in the shelling and residents were hiding in basements.

Local field hospitals were overwhelmed by arrivals, some of whom lay on the floor to receive treatment.

On one bed was an infant, his red and white striped sweater lifted up to allow medics to apply a defibrillator to his bloodied chest.

Eastern Ghouta is a key rebel bastion on the outskirts of Damascus, and has been under siege for nearly two years.

Since mid-2012, the government has carried out frequent air raids on rebel-held areas. It is accused by human rights groups of indiscriminately killing both civilians and insurgents.

Elsewhere in the country, the Observatory reported that at least 16 members of the Islamic State jihadist group were killed in strikes by the US-led coalition fighting the group.

The strikes in northeastern Hasakeh province hit a building containing a weapons and explosives depot, where secondary explosions were reported, the Observatory said.

More than 200,000 people have died in the Syrian conflict, which began with anti-government protests in March 2011 and escalated into a civil war.