As the advancement continues, a regime official cited a previous timetable believed to have been drawn up to guard against any change of policy by incoming US president, Donald Trump.
The Syrian regime says it wants to gain full control of Aleppo before the United State's president-elect Donald Trump takes office.
The siege of rebel-held eastern Aleppo by the regime has led to over 50,000 Syrians fleeing their homes in the last four days alone, according to the Syrian Observatory for Human Rights.
"If you don't leave these areas quickly you will be annihilated, save yourselves. You know that everyone has left you alone to face your doom and have offered you no help," read leaflets which were dropped by regime planes over rebel-held areas.
The Syrian regime and its backer Russia, both want to complete the operation before Trump takes power.
A regime official cited a previous timetable believed to have been drawn up to guard against any change of policy by the new president.
Trump has indicated that he may abandon support for rebels who have received military aid from the US, Turkey, Saudi Arabia and Qatar, and could even cooperate with Russia against Daesh in Syria.
France, another backer of opposition forces has called for an immediate UN Security Council meeting to discuss Aleppo.
"More than ever before, we need to urgently put in place means to end the hostilities and to allow humanitarian aid to get through unhindered," French Foreign Minister Jean-Marc Ayrault said.
The UN envoy for Syria, Staffan de Mistura, said he could not say how long eastern Aleppo would hold out.
"Clearly, I cannot deny - this is a military acceleration, and I can't tell you how long eastern Aleppo will last."
Aleppo has been the epicentre of the civil war that began in Syria in 2011 after the regime's crackdown on pro-democracy protests around the country. If captured, rights organisations said it would give Assad and his forces more control and power in the war-torn country.
Rebels Will Not Back Down
The unrelenting ground and air assault on eastern Aleppo by the regime threatens to snuff out the most important urban centre of the revolt against Assad.
Gaining full control of the city would be the biggest victory to date for the regime.
Russian and Iranian support for Assad turned the tide in his favour while rebels speaking from their besieged enclave of eastern Aleppo, said their backers including the US have left them to their fate.
Regime forces are attacking rebels from more than a third of the territory they now control in the city.
Rebels say they will not withdraw from eastern Aleppo, a clear indication that they plan to continue fighting regime forces.
"A withdrawal by the factions is rejected," head of the political office of the Aleppo-based Fastaqim rebel group, Zakaria Malahifji said.
"This is the decision of the factions. I spoke to them about everything that was tabled, and they said they would not withdraw, and other things may also happen."