The "Army of Conquest", a coalition of rebels and jihadists including the former Al-Nusra Front, said in a statement it would "double the number of fighters for this next battle".
"We announce the start of a new phase to liberate all of Aleppo" after a week of continuous fighting, the group said.
"We will not rest until we raise the flag of the conquest over Aleppo's citadel," it added.
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The group's fighters surged through regime territory on Saturday, breaking a three-week government siege in a major setback for the regime.
The rebel coalition opened a new route into the northern city's besieged eastern neighbourhoods, home to an estimated 250,000 people.
The operation triggered celebrations in eastern districts and sparked fears in regime-controlled western areas of the divided city of food and fuel shortages.
Rami Abdel Rahman, head of the Syrian Observatory for Human Rights, said it was one of the most significant setbacks for government forces since the conflict erupted in March 2011.
Syrian regime forces redeployed on Sunday to escape being surrounded in neighbourhoods they control in Aleppo, scene of some of the fiercest fighting in the civil war.