Syrian Observatory for Human Rights director Rami Abdel Rahman said the overnight clashes were "the fiercest since the fighting began in Aleppo and the closest yet to the intelligence base in the Zahra neighbourhood."
In an email, the Syrian Revolution General Commission, an activist network on the ground, said government aircraft "opened fire with heavy machine guns on the Al-Leyramun neighbourhood, and the outskirts of the air force intelligence base."
The Observatory said there had been casualties on both sides and civilians had fled the area.
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Government aircraft bombed rebel-held districts of the city throughout Friday and into Saturday, killing four rebels in the Rashidun district in the east of the city.
Islamist rebels shelled several government-held neighbourhoods, killing 10 people, five of them children, the Observatory said.
Rebels seized a big swathe of Aleppo in a major offensive in mid-2012 but the front line has since remained largely static.