At least three children were killed and 14 injured in a rebel rocket attack on a school in the government-held west of Aleppo city on Thursday, Syrian state media said.

A monitoring group said a child was also among at least eight people killed in government shelling on the rebel-held town of Douma outside Damascus.

"Three children were killed and 14 students were injured in a terrorist rocket attack on the national school in the Shahba neighbourhood of Aleppo," state news agency SANA reported.

The neighbourhood is in the western outskirts of the city, which has been roughly divided since mid-2012, when rebels seized its eastern half.

Rebels regularly fire crude homemade rockets into the west of the city, often killing civilians.

Government forces backed by ally Russia have waged an aerial and ground assault since late September to recapture eastern Aleppo, killing hundreds of civilians and destroying infrastructure including hospitals.

The deaths came a day after the UN children's agency UNICEF said 22 children had been killed along with six teachers in air strikes on a school in rebel-held Idlib province.

The strikes, carried out by either Russian or Syrian warplanes according to the Syrian Observatory for Human Rights, hit the village of Hass, prompting outrage from UNICEF director Anthony Lake.

"This is a tragedy. It is an outrage. And if deliberate, it is a war crime," he said, adding that the school complex had been hit repeatedly.

Outside Damascus meanwhile, at least eight people were killed on Thursday in government shelling on Douma in the rebel-held Eastern Ghouta region, the British-based Observatory said.

Douma is regularly targeted by government fire, and in recent months regime forces have waged an offensive in the area, which has also been under siege since 2013.

More than 300,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.

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