The fighting in the country's former economic powerhouse is some of the fiercest since the Syrian conflict arrived in the northern city in mid-2012.
Elsewhere, government forces launched a major operation to recapture Zabadani, the last opposition-held town in the Qalamun region near Damascus.
The Syrian Observatory for Human Rights reported heavy clashes in several parts of Aleppo's west side.
It said fighters from the Conquest of Aleppo alliance of mostly moderate forces had captured yesterday a former research centre being used as a military barracks.
A video online showed the capture, with fighters from one of the groups firing in the air, the three-starred flag of the Syrian uprising behind them.
The Observatory said government forces had tried unsuccessfully to recapture the facility overnight and launched air raids against it on Saturday, prompting the rebels to partially evacuate.
Conquest of Aleppo and a second rebel grouping, Ansar al-Sharia, which is dominated by Islamists and Al-Qaeda's local affiliate Al-Nusra Front, began operations against government-held districts of Aleppo this week.
The assault began Thursday, when Ansar al-Sharia attacked several neighbourhoods including Zahra, where an air force intelligence facility is based.
The coalition initially made progress, but was pushed back by government forces last night, the Observatory said.
The monitor said regime war planes carried out some 40 air strikes, and at least 29 Ansar al-Sharia fighters were killed yesterday.
There was no immediate toll for regime forces.
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