“We have just liberated Ashrafiyeh and the Syriac quarter,” a rebel fighter said, referring to areas which had been held by Kurdish militias and troops loyal to President Bashar al-Assad.
Rebels were still fighting around the Rahman Mosque district and trying to besiege a security building, he added.
Activists said at least 14 people were killed. It was not clear if the dead were fighters or civilians.
The Syrian Observatory for Human Rights, an opposition group monitoring the Syrian conflict, said Kurdish units were still fighting to stop the rebels from entering Ashrafiyeh.
Battles have engulfed Aleppo since late July, but a stalemate had developed, with snipers restricting movement of fighters and the two sides largely entrenched on frontlines.
Assad’s government was expected to make a statement later in the day on whether it accepts the temporary ceasefire advocated by U.N.-Arab League envoy Lakhdar Brahimi.
Syrian authorities said on Wednesday they were still studying the plan, but Russia’s envoy to the United Nations said Damascus had indicated to Moscow that it would agree to it.