In the Syrian city of Aleppo, the small bodies of dead children are piling up in increasing numbers.

At least a dozen children have been killed on both sides of the city as regime and rebel forces step up their attacks on civilian targets.

Just after midnight on Saturday, a barrel bomb dropped on the East Aleppo's Sakhour district by Syrian regime forces reportedly killed four children and both their parents.

Two medics told the Reuters news agency the al-Baytounji family suffocated to death because the barrel bomb had been laced with chlorine gas.

Graphic video posted online by Syrian activists showed the lifeless bodies of four small children laid out on the ground, their lips blue with dark marks around their open eyes. Apart from the discolouring to their faces, they did not appear have any obvious wounds.

The Syrian Observatory for Human Rights (SOHR), which monitors the war, confirmed the bombing but could not confirm that chlorine gas was used. Damascus has denied use of the gas, which would contravene the international Chemical Weapons Convention.

A few hours after the video of the suspected gas attack emerged, the Syrian state news agency reported that the Saria Hasoun school, in the al-Farqan district in Government-held West Aleppo, had been hit by rebel shelling.

Schools were destroyed by heavy shelling in Aleppo. ( Twitter: Sophie McNeill )

Video and photos of the scene showed bloodied schoolbooks, upturned desks and distraught young children. Photos of small bodies wrapped in shrouds were posted on social media.

A Syrian girl is one of those injured after shelling hit her school in Aleppo. ( Supplied )

SOHR said the attack on the school killed at least eight children, aged from six to 12 years, and two adults.

Hundreds of people have been killed in East Aleppo since November 15, as the Syrian Government and its allies attempt to quash resistance in the rebel-held eastern zone.

An official with a rebel group based in east Aleppo told Reuters there were still no working hospitals there on Sunday, a day after the World Health Organisation reported that bombing had put them all out of action.

The UN's envoy Staffan de Mistura met Foreign Minister Walid Muallem in Damascus for talks on the escalating violence, but was rebuffed on a truce proposal that would allow the opposition to administer the city's rebel-held east.

Aid agencies fear that "instead of a humanitarian or a political initiative" there would be "an acceleration of military activities" in eastern Aleppo and elsewhere, Mr de Mistura told journalists.

"By Christmas ... due to military intensification, you will have the virtual collapse of what is left in eastern Aleppo; you may have 200,000 people moving towards Turkey — that would be a humanitarian catastrophe," he said.

ABC/Reuters