The UN human rights office says it has received reports of Syria's pro-government forces killing at least 82 civilians in eastern Aleppo. UN human rights office spokesman Rupert Colville says the reports say pro-government forces entered homes and killed some civilians "on the spot" in four different neighbourhoods in the increasingly-shrinking rebel enclave.

A man carries a child as he flees deeper into the remaining rebel-held areas of Aleppo Abdalrhman Ismail/Reuters

Colville expressed deep fear of retribution against thousands of civilians still believed to be holed up in a "hellish corner" of less than a square kilometre of the opposition-held area. "The reports we had are of people being shot in the street trying to flee and shot in their homes", he said.

The commander of a rebel group in Aleppo is urging the US and Turkey to move quickly to save civilians in what remains of the opposition's eastern Aleppo enclave from an assault by the government and its allies. "My message is that they must take a decision to save these people who are stuck here, these civilians, these children," Abu Ali Saqour, the commander of the Jabha Shamiya group, told Reuters, the sound of explosions audible in the background as he spoke via Whatsapp from eastern Aleppo.

"No state has helped these people in any way, my message to the world is to get these people out of this disaster-stricken city, at least the civilians," he said, singling out the US and Turkey as governments with the power to do something. "Any state with power in its hands must take a decision as soon as possible to evacuate these people," he said.

The Jabha Shamiya rebel group is fighting in Aleppo under the banner of the Free Syrian Army, and is one of the factions that has received support from states opposed to Assad, including Turkey.

On the front lines, he said: "The situation is, God willing, good", describing the new positions taken up by the fighters as solid and steadfast. "The situation on the fronts is much better," he said. But bombardment is continuing. "The bombardment is not on the front lines, the greater burden of the bombardment is on the civilians, and this is what is causing a burden on us," he said.

The Syrian army and its allies have taken full control over all the Aleppo districts abandoned by rebels during their retreat in the city, a Syrian military source said. Rebel defences collapsed on Monday, leading to a broad army advance across more than half of the remaining insurgent pocket in Aleppo and a retreat of opposition fighters to a few districts on the west bank of the Queiq River.

Recapturing the entire rebel pocket of Aleppo will constitute the biggest battlefield victory yet for President Bashar al-Assad and his military coalition of Syrian troops, the Russian air force, Iran, and Shia militias. Its loss will leave the rebels without a significant presence in any of Syria's main cities. They still hold much of the countryside west of Aleppo and the province of Idlib, also in north-west Syria.