Syrian government forces have taken control of more than half of Aleppo’s rebel districts after fierce bombardments and ground advances forced tens of thousands to flee.

The UN envoy for Syria, Staffan de Mistura, said on Saturday he anticipated a “terrible battle” for complete control of the city.

Jets and artillery pounded besieged eastern districts as Syrian troops and allied fighters from Iraq, Iran and Lebanon pushed further into the city, securing parts of Tariq al-Bab and the airport road to the east of Aleppo, the Syrian Observatory for Human Rights said.

Some of the areas taken by government forces had been held by opposition fighters since 2012, as forces loyal to Bashar al-Assad undermined the stalemate that kept Aleppo divided for four years.

“The noose is tightening quickly,” Mohammed Abu Jaafar, a medical official in eastern Aleppo, told the Associated Press. “Our resources are also running low and beginning to disappear.”

Mistura said he feared the opposition would not be able to withstand the attacks for much longer, Reuters reported.

“The fact is that Aleppo is not going to stay that long,” he told a conference in Rome. “I was feeling it would be a terrible battle ending up by Christmas-New Year. I hope the battle will not take place, that there will be some type of formula.”

Around a quarter of a million people had stayed on in besieged Aleppo, but more than one in 10 fled last week, the UN estimated.

About 19,000 people went to Syrian government-controlled areas, around 10,000 to an enclave held by Kurdish troops, and 5,000 moved deeper into opposition-held areas. Nearly two-thirds of those displaced are children.

Those left in the opposition-held areas of the city have little hope of relief as winter intensifies, food stocks decline and new arrivals cram into the homes and buildings that remain standing.

“I left everything, even my clothes, it is so bad, and so cold,” said Fatema, whose tweets about life under siege with her three children have built up a following of nearly 200,000 people.

This is my reading place where I wanted to start reading Harry Potter but it's bombed. I will never forget. - Bana pic.twitter.com/6fXX2Me8ZB — Bana Alabed (@AlabedBana) November 29, 2016

Their home was hit last week and they had to take shelter with friends. “Hello my friend, how are you. I am on the run now, I fear being killed. Please save us. Thank you,” Bana Alabed said in a short video shared by the Harry Potter author, JK Rowling.

The family fear they may have been targeted because their tweets have such a wide audience and, like many in the city, they believe it would be too dangerous to cross to areas under the control of a government known for harsh treatment of anyone it suspects of opposition.

The Russian foreign minister, Sergei Lavrov, said on Saturday that Moscow was ready for talks with the US about a complete withdrawal of rebels from Aleppo, but rebel groups have insisted they will fight to the death.

“I asked the factions, they said: ‘We will not surrender’,” Zakaria Malahifji, the head of the political office of the Aleppo-based Fastaqim faction, told Reuters. “The military commanders in Aleppo said: ‘We will not leave the city’.”