The Britain-based Syrian Observatory for Human Rights said the crude explosive devices hit three areas of Aleppo, prompting the rebels to fire rockets into regime-held western parts of the city.
The violence erupted at sunset, breaking the calm that had prevailed throughout the day, the monitor added.
Syrian regime ally Russia had announced a two-day truce in Aleppo, but hours after it took effect yesterday barrel bombs and air strikes hit the eastern side, and rebels retaliated with rockets.
Aleppo has seen some of the worst fighting in a conflict that has killed more than 280,000 people since it began in March 2011 with anti-government protests.
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The truce was announced by Russia after US Secretary of State John Kerry warned Moscow that Washington's patience was running out over breaches of a nationwide ceasefire.
And yesterday a senior US defence official accused Russia of bombing US-backed fighters in Al-Tanaf near Syria's border with Iraq.
The Observatory said two fighters opposed to the Islamic State group were killed in the strikes which it said targeted a meeting at which they were coordinating the fighting against IS in Syria and Iraq.