The facades of many buildings overlooking the square were ripped off and a deep crater was gouged in the road. The Syrian Observatory for Human Rights said 48 people were killed, mostly from the security forces, while SANA put the death toll at 31.
Wednesday's attacks in Aleppo followed last week's bombing of the military staff headquarters in Damascus, another strike by Assad's outgunned opponents against bulwarks of his power.
In July, rebels killed four of Assad's senior security officials including Assad's brother-in-law, the defence minister and a general in a Damascus bombing which coincided with a rebel offensive in the capital.
Government forces have since pushed rebel fighers back to the outskirts of Damascus. But they have lost control of swathes of northern Syria as well as several border crossings with Turkey and Iraq and failed to push the fighters out of Aleppo.
A pro-Assad Lebanese paper said on Tuesday that Assad was visiting the city to take a first-hand look at the fighting and had ordered 30,000 more troops into the battle.
Many rich merchants and minority groups in Aleppo, fearful of instability, remained neutral while protests spread through Syria. But rebels from rural Aleppo swept into the city in July and still control districts in the east and south.
Opposition activists say 30,000 people have been killed across the country in the 18-month-old uprising, which has grown into a full-scale civil war with sectarian overtones and threatens to draw in regional Sunni Muslim and Shi'ite powers.