"The number of martyrs in the massacre carried out by terrorists in Aleppo has risen to 20 dead and more than 100 hurt," state television said in a breaking news alert.
The Syrian Observatory for Human Rights also reported the rocket fire, putting the toll at 13, including two children, and adding that it was expected to rise.
The group also said around 100 people were wounded, among them 20 children.
The Britain-based monitor said rebels had fired some 250 rockets at several districts in western Aleppo city in just four hours, causing massive damage including the collapse of an entire building.
One stretcher carried the body of an adult whose face was covered with blood, and a dead child, ghostly with white dust.
Once Syria's economic powerhouse, Aleppo has been ravaged by the conflict that began with anti-government protests in March 2011, before spiralling into a civil war.
The city has been divided between government control in the west and rebel control in the east since shortly after fighting spread to it in mid-2012.
Regime forces regularly bombard the eastern side from the air, dropping crude barrel bombs that rights groups say are indiscriminate and can kill dozens of civilians at a time.
More than 230,000 people have been killed in Syria since March 2011, according to the Observatory.
The United Nations envoy for Syria, Staffan de Mistura, is currently visiting Damascus to brief government officials on talks he has held on ways to end the conflict.
Ahead of his visit, his spokesman said he would raise the "unacceptable" use of barrel bombs by the regime.
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