A total of 20 people have been killed as battles dragged the contested city of Aleppo in northern Syria deeper into chaos for a 12th straight day.

The new bloodshed came as the diplomatic focus moved to Moscow, where the UN envoy for Syria raced to restore a partial ceasefire in the civil war that would include Aleppo.

The envoy, Staffan de Mistura, met with Russian Foreign Minister Sergey Lavrov a day after meeting US Secretary of State John Kerry in Geneva.

Aleppo has been at the centre of the conflict for the past two weeks, shattering a limited ceasefire that began in late February.

Tuesday's attack on the Dubeet hospital in the government-held central Muhafaza area that killed four people echoed an airstrike on a hospital on the rebel-held side of the city that killed about 50 civilians nearly a week ago.

About 280 civilians have died in the city in the last 12 days, according to the UK-based Syrian Observatory for Human Rights, a monitoring group of local activists.

Rebel shelling of the government side of the city killed 20 people and injured 100, according to Mohammad Hazzouri, head of the city's Health Directorate. The Observatory said 19 had died.

Activists reported government bombardment killed two civilians and wounded several others on the rebel side.

Syrian information minister Omran al-Zoubi warned rebels they would face harsh retaliation for shelling civilian areas.

Direct clashes between government and rebel forces on Aleppo's outskirts accompanied the shelling inside, foreshadowing a full-scale conflict unless a ceasefire is negotiated.

An opposition media activist outside Aleppo said rebels were waging a counter-offensive against pro-government forces on the western side of the city.

Nazeer al-Khatib said government forces attacked the rebels first, prompting rebel factions, headed by the Nour el-Din al-Zinki brigade, to retaliate.

He could not confirm reports the rebels had taken over the compound, a former mall that has turned into a frontline position in the suburb of New Aleppo.

Major Jamil Saleh, leader of Tajammu Al-Ezzah army, said his group was fighting in Aleppo.

The rebel group, which falls under the Free Syrian Army (FSA) and has been vetted and receives support by the US, ordinarily wages battles in the central province of Hama and in rural Latakia.

"Most of the FSA factions are taking part in the battle in the heart of Aleppo," he said.

"The city is important for all Syrians. It is important economically, militarily and is the commercial capital of Syria. Letting go of Aleppo is a treason to the revolution."

An official with the ultra-conservative Ahrar al-Sham group said the Fatah Army, or Army of Conquest coalition, has been revived to carry out military operations in the near future against government forces and their allies in northern Syria, mostly in Aleppo province.

The coalition, which includes Ahrar al-Sham, al-Qaida's branch in Syria known as the Nusra Front and the Salafi-Jihadi Jund al-Aqsa faction, was one of the most effective forces against President Bashar Assad's troops last year. It captured wide areas in the northern province of Idlib from government forces.

The Ahrar al-Sham official told Associated Press via text message that the Fatah Army will carry out an act in Aleppo but added that the coalition had no role in Tuesday's attacks.

The coalition was suspended before Syria's indirect, UN-sponsored peace talks resumed in January in Geneva because it included extremists groups such as the Nusra Front that oppose the peace process and the UN considers terrorist organisations.