A fourth explosion a few hundred meters (yards) away also struck near the edge of the Old City, a UNESCO World Heritage site that has seen fierce street fighting between rebels and government forces, The Associated Press reported.
There was no immediate claim of responsibility, but the government blamed armed terrorists and said the blasts were caused by suicide bombers.
The bloodshed comes amid growing concerns that extremists such as Al-Qaeda are making inroads inside Syria.
Long free of the violence that has engulfed much of the rest of the country, Aleppo in the past two months has become a key battleground between government forces and foreign-backed insurgents fighting against the government President Bashar al-Assad. The opposition launched an initial offensive on the city, Syria's largest and a commercial hub, in July. Large swaths of the ancient city have been shattered.
Over the weekend, a fire sparked by fighting tore through Aleppo's centuries-old covered market in the Old City, burning more than 500 shops. At 12 kilometers (7.5 miles), it is the Middle East's longest souk and is part of Aleppo's old center that was added in 1986 to UNESCO's list of World Heritage sites.
Syria has been experiencing unrest since March 2011. Damascus says outlaws, saboteurs, and armed terrorists are the driving factor behind the unrest and deadly violence while the opposition accuses the security forces of being behind the killings.
Western states have been calling for President Assad to step down. However, Russia and China are strongly opposed to the Western drive to oust Assad.
The Syrian government says that the chaos is being orchestrated from outside the country, and there are reports that a very large number of the armed militants are foreign nationals, mostly from Egypt, Algeria, Saudi Arabia, and Afghanistan.
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