United Nations Secretary-General Ban Ki-moon is alarmed by unverified reports of atrocities against a large number of civilians, including women and children, in Syria's Aleppo, his spokesman has said.

"The Secretary-General is conveying his grave concern to the relevant parties. He has instructed his Special Envoy for Syria to follow up urgently with the parties concerned," UN spokesman Stephane Dujarric said in a statement.

The statement comes as the Syrian army and its allies are in the "final stages" of recapturing Aleppo after a sudden advance that pushed rebels to the brink of collapse in an ever-shrinking enclave, according to a Syrian general.

A Reuters journalist in the government-held zone said the bombardment of rebel areas of the city had continued non-stop overnight, and a civilian trapped there described the situation as resembling "Doomsday".

"The battle in eastern Aleppo should end quickly. They (rebels) don't have much time. They either have to surrender or die," Lieutenant General Zaid al-Saleh, head of the government's Aleppo security committee, told reporters in the recaptured Sheikh Saeed district of the city.

Rebels withdrew from all districts on the east side of the Aleppo river after losing Sheikh Saeed in the south of their pocket in overnight fighting, the British-based Syrian Observatory for Human Rights said.

It meant their rapidly diminishing enclave had halved in only a few hours and Observatory director Rami Abdulrahman described the battle for Aleppo as having reached its end.

"The situation is extremely difficult today," said Zakaria Malahifji of the Fastaqim rebel group fighting in Aleppo.

An official from Jabha Shamiya, a rebel faction that is also present in Aleppo, said the insurgents might make a new stand along the west bank of the river.

"It is expected there will be a new front line," said the official, who is based in Turkey.

The rebels' sudden retreat represented a "big collapse in terrorist morale", a Syrian military source said.

Syrian President Bashar al-Assad, backed by Russia, is now close to taking back full control of Aleppo, which was Syria's most populous city before the war and would be his greatest prize so far after nearly six years of conflict.

The Russian Defence Ministry said that since the start of the Aleppo battle, more than 2,200 rebels had surrendered and 100,000 civilians had left areas of the city that were controlled by militants.

"People run from one shelling to another to escape death and just to save their souls ... It's doomsday in Aleppo, yes doomsday in Aleppo," said Abu Amer Iqab, a former government employee in the Sukkari district in the heart of the rebel enclave.

State television footage from Saliheen, one of the districts that had just fallen to the army, showed mounds of rubble and half-collapsed buildings, with bodies still lying on the ground and a few bewildered civilians carrying children or suitcases.

While Aleppo's fall would deal a stunning blow to rebels trying to remove Mr Assad from power, he would still be far from restoring control across Syria.

Swathes of the country remain in rebel hands, and on Sunday the self-proclaimed Islamic State group retook the ancient city of Palmyra.

Tens of thousands of civilians remain in rebel-held areas, hemmed in by ever-changing front lines, pounded by air strikes and shelling, and without basic supplies, according to the Observatory.

Yesterday, rebel groups in Aleppo received a U.S.-Russian proposal for a withdrawal of fighters and civilians from the city's opposition areas, but Russia said no agreement had been reached yet in talks in Geneva to end the crisis peacefully.

The rebel official blamed Russia for the lack of progress in talks, saying it had no incentive to compromise while Mr Assad was gaining ground.

"The Russians are being evasive. They are looking at the military situation. Now they are advancing," he said.

The US National Security Council also said, in a message passed on by the American mission in Geneva, that Russia had rejected a ceasefire.

"We proposed an immediate cessation of hostilities to allow for safe departures and the Russians so far have refused," it said in a statement.