Nine of the victims, including women and children, were killed in air raids in the Aleppo districts of Tariq al-Bab and al-Salehin, Efe news reported.
Another three people were killed in Manbech in bombings led by the international coalition against the Islamic State (IS).
A fourth person died as a result of shelling in the same town.
Armed opposition factions on Tuesday launched an attack against government-controlled areas after President Bashar al-Assad's forces cut the main weapons supply route to the rebel-held districts in eastern Aleppo.
The escalation of violence in the province of Aleppo coincided with a 72-hour ceasefire called for by the Syrian government on July 6, as the country celebrated Eid ul-Fitr, marking the end of the holy month of Ramadan.
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