Between 10,000 and 13,000 civilians have fled from eastern Aleppo in the past 24 hours
The battle for control of Aleppo has reached its end, a UK-based monitor has said.
The director of the Syrian Observatory for Human Rights, Rami Abdulrahman, said rebels have withdrawn from the last six neighbourhoods they held in the city.
It follows fierce fighting and sweeping gains by the Syrian army into the previously rebel-held east of the city.
A Reuters journalist based in the government-held part of the city said overnight bombardment of the east had been the most intense for days.
As day broke, the Russians, Syrians and the Observatory claimed ever diminishing amounts of territory were under the control of rebels who had held the territory for over four years.
The Syrians' last claim was that it held 98% of areas previously held by the rebels.
At 11.50pm Irish time, a Syrian rebel spokesman admitted opposition fighters were retreating - and said the collapse of the enclave was "terrifying".
There has been no comment from the Syrian government or their Russian allies about the Observatory's claim beyond what was said earlier.
Syria's chief opposition coordinator Riad Hijab said that defeat in Aleppo would not weaken the resolve of Mr Assad's opponents.
"If Assad and his allies think that a military advance in certain quarters of Aleppo will signify that we will make concessions, then (I say) that will not happen," he said.
Between 10,000 and 13,000 civilians have fled from eastern Aleppo in the past 24 hours, bringing the total number to have escaped the fighting there to an estimated 130,000, the Observatory and other reports said.
The Russian defence ministry said 100,000 civilians are left in eastern Aleppo.
Amid reports that hundreds of men fleeing the east of the city have gone missing, pictures have emerged that appeared to show men from the former rebel-held areas being conscripted into the Syrian army.
Military service in Syria is mandatory for men over the age of 18.
Reuters said its photographer on the scene was told by the Syrian military forces present at the time the photographs were taken that that the men were on their way to be conscripted.
The apparent Syrian victory in Aleppo follows a major offensive by government forces, backed by Russia, that began in mid-November.
Overnight, three officials with rebel groups in Aleppo told Reuters they had received a letter, guaranteeing safe passage, if they left the city.
The US-backed proposal would have ended a siege that has lasted several months.
Moscow denied any such deal, which apparently followed talks between the US and Russia in Geneva to find a way out of the crisis that has left tens of thousands of civilians trapped amid heavy fighting.
One of the officials with rebel groups said on Monday morning: "They sent us a letter, they are saying to safeguard the civilians...you can leave in an honourable way to any place you choose and the Russians will pledge publicly that nobody will be harmed or stopped.
"We have yet to give a response."
Russian Deputy Foreign Minister Sergei Ryabkov said his country was working towards the safe extraction of people from Aleppo.
Russia's Defence Ministry said 2,200 rebels had laid down their weapons since the start of the renewed offensive.
The UK-based Observatory added that at least 413 civilians have been killed in east Aleppo since the latest offensive began on November 15th, and 139 have been killed in the city's west by rebel rocket fire.
Analysts said a victory for the Syrian government in Aleppo would be a major "triumph" for Mr Assad at a time when his forces continue to face challenges across the country.