"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.
- Food trucks enter Aleppo -
Rebel units on Saturday pushed northeast into the Ramussa district where they linked up with other insurgents who had fought from inside the city.
Video footage seen by AFP showed fighters on Sunday evacuating a small group of civilians, mostly women and children, from Ramussa.
Rebels also brought seven pick-up trucks full of fruit and vegetables into the eastern sector of Aleppo which had been under government siege since July 17, an opposition fighter said.
The Observatory's Abdel Rahman said the route into eastern districts was open only to fighters and was still not secure enough to evacuate civilians from the area.
The rebel advance now puts the estimated 1.2 million people in government-held districts under opposition encirclement, he added.
"The western districts of Aleppo are now besieged. There are no safe routes for civilians in government-held districts to use to get into or out of the city," he told AFP.
- Preparing for siege -
Families in western neighbourhoods meanwhile began to stock up on food and water in preparation for a siege but complained about the rising cost of basic supplies.
"Unfortunately, after the road was cut, the price of a loaf of bread immediately shot up from 200 to 800 Syrian pounds," said Walaa Hariri, a 48-year-old mother of three from the Furqan district.
"I sent my sons to school but they are all nervous, and the teachers replaced their regular lessons with courses on what to do if there is shelling," she said.
A man aged 37 who declined to be identified said he had "faith in the army, but I can't help being scared".
"Food is already getting more expensive and the coming days risk being very difficult," he added.
The battle for Aleppo has raged since mid-2012 and is among the fiercest so far in Syria's chaotic multi-front war, which has killed more than 280,000 people since it erupted five years ago.
Pope Francis on Sunday denounced the "unacceptable" number of civilian victims in Aleppo, mentioning in particular the number of children killed in the conflict.
Since the opposition alliance launched its offensive on southern Aleppo on July 31 at least 130 civilians and hundreds of fighters from both sides have been killed, said the Observatory.
On Monday, the UN Security Council is due to hold an informal meeting at 1400 GMT on the Aleppo crisis.
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"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.
- Food trucks enter Aleppo -
Rebel units on Saturday pushed northeast into the Ramussa district where they linked up with other insurgents who had fought from inside the city.
Video footage seen by AFP showed fighters on Sunday evacuating a small group of civilians, mostly women and children, from Ramussa.
Rebels also brought seven pick-up trucks full of fruit and vegetables into the eastern sector of Aleppo which had been under government siege since July 17, an opposition fighter said.
The Observatory's Abdel Rahman said the route into eastern districts was open only to fighters and was still not secure enough to evacuate civilians from the area.
The rebel advance now puts the estimated 1.2 million people in government-held districts under opposition encirclement, he added.
"The western districts of Aleppo are now besieged. There are no safe routes for civilians in government-held districts to use to get into or out of the city," he told AFP.
- Preparing for siege -
Families in western neighbourhoods meanwhile began to stock up on food and water in preparation for a siege but complained about the rising cost of basic supplies.
"Unfortunately, after the road was cut, the price of a loaf of bread immediately shot up from 200 to 800 Syrian pounds," said Walaa Hariri, a 48-year-old mother of three from the Furqan district.
"I sent my sons to school but they are all nervous, and the teachers replaced their regular lessons with courses on what to do if there is shelling," she said.
A man aged 37 who declined to be identified said he had "faith in the army, but I can't help being scared".
"Food is already getting more expensive and the coming days risk being very difficult," he added.
The battle for Aleppo has raged since mid-2012 and is among the fiercest so far in Syria's chaotic multi-front war, which has killed more than 280,000 people since it erupted five years ago.
Pope Francis on Sunday denounced the "unacceptable" number of civilian victims in Aleppo, mentioning in particular the number of children killed in the conflict.
Since the opposition alliance launched its offensive on southern Aleppo on July 31 at least 130 civilians and hundreds of fighters from both sides have been killed, said the Observatory.
On Monday, the UN Security Council is due to hold an informal meeting at 1400 GMT on the Aleppo crisis.
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