President Bashar al-Assad's forces held more than 90 percent of the onetime opposition stronghold of east Aleppo and appeared on the verge of retaking the entire city, a monitor and military official said.
A Syrian military official in Aleppo told AFP the "operation in eastern neighborhoods is entering its final phase," as fierce clashes were reported in the few districts still under rebel control.
The fall of Aleppo would be the worst rebel defeat since Syria's conflict began in 2011, and leave the government in control of the country's five major cities.
The Syrian Observatory for Human Rights monitoring group reported that the army had captured southeast Aleppo's large Sheikh Saeed district.
Syrian official media confirmed Sheikh Saeed had been retaken, with state television showing what it said was live footage from the neighborhood.
The rebels withdrew from six more districts in the face of advancing government troops, the Britain-based Observatory said.
The retreat leaves opposition fighters confined to just a handful of neighborhoods in southeast Aleppo, the largest of them Sukkari and Mashhad.
'A total collapse'
"The battle of Aleppo has reached its end. It is just a matter of a small period of time ... it's a total collapse," said Observatory director Rami Abdel Rahman.
In the Mashhad neighborhood, residents fleeing the army advance crowded the streets, witnesses said.
Displaced civilians — many hungry after fleeing without food — sat on pavement or lay on the street with nowhere else to go, they said.
An AFP correspondent in the government-held west of Aleppo said the bombardment of rebel areas could be heard and was among the heaviest in recent days.
"The regime is advancing in east Aleppo under gunfire, missiles and shelling," Bassam Mustafa from the political office of the Nureddin al-Zenki rebel group, in Aleppo, told reporters.
"The fighters [rebels] are retreating under pressure and the situation is very bad," he said.
State television also aired live footage from inside Salhin district, one of the areas fully retaken on Monday, showing widespread destruction.
Buildings were missing entire sections, and roads were littered with rubble and pitted with enormous craters.
Terrified residents have poured out of rebel-held neighborhoods as the army advanced since beginning its operation on Nov. 15.
The Observatory said Monday another 10,000 people had fled rebel areas in the previous 24 hours, bringing the total number of those who have left — mostly to government-held territory — to 130,000.
Syria's rebels seized control of east Aleppo in 2012, a year into an uprising that began with anti-government protests but spiraled into a civil war after a regime crackdown.
The war has become a complex multifront conflict, drawing in proxy powers and jihadists such as the Islamic State group, which on Sunday retook the symbolically important city of Palmyra nine months after being expelled.
IS managed to again seize control of Palmyra — where the jihadists carried out a campaign of destruction against famed ancient ruins — despite heavy Russian airstrikes and the arrival of Syrian troop reinforcements.
On Monday, the jihadists were advancing south and west of Palmyra, clashing with the army near the town of Al-Qaryatain, the Observatory said.
More than 300,000 people have been killed in Syria's war, and over half the country displaced.
The government assault on Aleppo has killed at least 415 civilians since mid-November, according to the Observatory. Another 130 civilians have been slain in rebel fire on the city's west over the same period, it says.
Diplomatic efforts to end the conflict have repeatedly failed.
Russia last week said talks were underway with US officials on securing a ceasefire and the withdrawal of all rebel forces from Aleppo.
But despite a series of high-level meetings, there was no progress in halting the fighting.
Moscow is a key Assad ally and launched an air war in support of his forces last year, while Washington and other Western nations have supported rebel forces battling the regime.
French Foreign Minister Jean-Marc Ayrault said Monday the latest round of Russia-US talks over the weekend failed "because there is double-talk and a sort of permanent lie" on Russia's part.
"On the one hand they say, 'Let's talk, let's talk and get a ceasefire,'" Ayrault said. "On the other hand, they continue the war ... aimed at saving Assad and capturing Aleppo."