"Shells fired... By rebel groups at districts under regime control left 19 dead, including three children, and 120 wounded," said the Syrian Observatory for Human Rights head, Rami Abdel Rahman.
The official SANA news agency reported 16 dead and 86 wounded by "fire from the terrorist groups Al-Nusra Front (Syrian branch of Al-Qaeda) and its allies" on at least five residential districts.
The Observatory also reported four people including a child killed by regime fire into rebel-held neighbourhoods of the city.
Several districts of the city, once Syria's commercial hub, have also seen sporadic fighting between government forces and rebel groups.
Rebel-held neighbourhoods in eastern Aleppo have had their water and electricity supplies cut by bombardment, an AFP journalist said.
The fighting severely threatens a February 27 ceasefire brokered jointly by the United States and Russia.