BEIRUT — Thousands of people fled for their lives on Monday as rebel fighters lost a large stretch of territory in the northern Syrian city of Aleppo to government forces, in what could prove to be a turning point in the conflict.

Residents described desperate scenes of people being killed by shells as they searched for shelter after their homes came under the heaviest bombardment yet in years of airstrikes and shelling.

The air raids have destroyed entire neighborhoods of the rebel-held half of the divided city, once Syria’s largest and an industrial hub. More than 250,000 people are believed trapped there with limited access to food, water, and medical supplies. They include more than 100,000 children, the United Nations has said.

At least 4,000 people have fled from the rebel-held eastern districts to the government-controlled western side of the city and have been registered with the Syrian Arab Red Crescent in Jibreen, a neighborhood there, Jens Laerke, the spokesman for the UN office for humanitarian affairs, said Monday.

Aid groups said an additional 6,000 people reached the Kurdish-controlled area of Sheikh Maksoud.

The number of civilian casualties in the latest offensive is unknown. Eastern Aleppo’s rebel-run council estimates that at least 500 civilians have been killed and 1,500 wounded.

As the rebels absorbed the harshest blow since they seized more than half the city four years ago, it seemed increasingly likely that President Bashar Assad would eventually manage to take back all of Aleppo.

That would give the Syrian government control of the country’s five largest cities and most of the more-populous west, leaving the rebel groups that are most focused on fighting Assad with only the northern province of Idlib and a few isolated pockets in the provinces of Aleppo and Homs and around the capital, Damascus.

Throughout the day, government troops, backed by allied militias from Iran and the militant group Hezbollah, advanced from the east and north into the rebel-held areas of Aleppo. That included Hanano, one of the first areas to fall, in 2012, and Sakhour.

Kurdish-led militias were also involved in the fight, advancing from the west, from the Kurdish-controlled neighborhood of Sheikh Maksoud, taking the rebel-held district of Sheikh Fares.

Kurdish militias have staked out areas of de facto autonomy in parts of the country but are not entirely aligned with either the government or the rebels. The state media and opposition activists have portrayed them in the current fighting in Aleppo, however, as working with the government to fight rebels.

The Kurdish militias have clashed previously with rebels in Aleppo, who shelled the Sheikh Maksoud area.

If the government takes back the whole city, large parts of Syria would still remain outside its control, as Kurdish groups and the Islamic State hold most of the eastern half of the country. But it could effectively spell the end of the Syrian insurgent movements that sprang up against Assad after a crackdown on protests in 2011.

“It’s like doomsday,’’ said Zaher al-Zaher, an antigovernment activist in eastern Aleppo who could communicate only in short bursts of text messages, as Internet connections were failing.

Hisham al-Skeif, a member of a local council in the rebel-held eastern districts of Aleppo, said he was scrambling to find housing for families in areas that had been recaptured in the past day.

“The problem today, in this moment, is not water and food,’’ he said, at one point choking with tears. “We are threatened with slaughtering, slaughtering.’’

The advances shattered a standoff that had lasted months, after government forces surrounded and besieged the rebel-controlled parts of the city this year, closing off regular access to food, medicine, and other supplies.

The government and its Russian allies made several offers for civilians and fighters to leave under government supervision, but there were few takers. People in eastern Aleppo said they did not trust the government to keep them safe, and government officials said the rebels were not allowing them to leave.

But on Monday, there appeared to be little room for compromise.

Government soldiers posted a video of themselves playing the drums in celebration on the outskirts of rebel-held areas, as leaflets were dropped, telling those inside to flee or face death.

“We won’t have any mercy to those who confront the Syrian Arab army,’’ one flier read, “but for those who will return to normal life, all the essentials of life will be secured.’’

Another leaflet told rebels to abandon hopes that insurgents outside the city would break the siege.

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