The “Army of Conquest”, a coalition of rebels and jihadists, said 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 in a statement.
“We will not rest until we raise the flag of the conquest over Aleppo’s citadel,” it added.
The group’s fighters surged through regime territory on Saturday, breaking a government siege in a major setback for the regime and opening 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 the rebel action was one of the most significant setbacks for government forces since the conflict erupted in March 2011.
“Despite more than 600 Russian strikes, the regime forces were not able to hold on to their positions,” he said.
Steadfast regime ally Moscow has provided air support for forces loyal to President Bashar al-Assad since last September.
Official media denied the siege had been broken but implicitly admitted that regime forces were on the defensive, reporting new air raids Sunday and saying that pro-government areas were facing shortages in the country’s ravaged second city.
State television said on Sunday: “Our forces have redeployed after absorbing the attack of thousands of mercenaries, and the army has found a new route to allow food and gas in.”
The official SANA news agency later quoted a military source as saying that “the air force conducted 21 sorties and struck the terrorists 86 times in south and west Aleppo in the last 12 hours”.
An AFP correspondent said air raids bombarded rebel-held areas of Aleppo, with the Britain-based Observatory saying the strikes were carried out by Russian and Syrian aircraft.
The Observatory also reported intermittent clashes on the city’s southern edges, where rebels overran buildings in a military academy on Saturday.