The Britain-based Observatory for Human Rights said Sunday that at least 16 rebels are among those who died in the overnight combat with President Bashar Assad's forces.
At least 13 civilians were also killed when government aircraft dropped barrel bombs on the city's three rebel-held districts Saturday, the Observatory said.
Another activist group, the Syria-based Local Coordination Committees also reported heavy fighting in Aleppo, saying Assad's warplanes launched fresh airstrikes there on Sunday.
Aleppo, Syria's largest city and its onetime commercial center, has been a key front in the civil war since July 2012 when rebels launched an offensive there.
AP