Pro-government forces took Sheikh Saeed in the south of the shrinking rebel pocket and Saliheen and Karam al-Daadaa on its eastern flank, a Syrian military source said, describing the advances as "a big collapse in terrorist morale".

Syrian President Bashar al-Assad now stands ready to take back full control of Aleppo, which was Syria's most populous city before the war and would constitute his greatest prize so far after nearly six years of conflict.

Rebel groups in Aleppo received a US-Russian proposal on Sunday for a withdrawal of fighters and civilians from the city's opposition areas, but Moscow said no agreement had been reached yet in talks in Geneva to resolve the crisis .

While Aleppo's fall would deal a stunning blow to rebels trying to remove Assad from power, he would still be far from restoring control across Syria. Swathes of the country remain in rebel hands, and on Sunday Islamic State retook Palmyra.

"The bombardment did not stop for a moment overnight," said a Reuters journalist in the government-held zone of the city, describing it as the most intense for days.

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, the Syrian Observatory for Human Rights, a British-based monitoring group, said.

The Observatory reported that the Sheikh Saeed district had fallen to the army in fighting on Sunday night and early on Monday and added that it was firing on the districts of Karam al-Daadaa and Fardous.

An advance by the army into those districts would take them into the heart of the area held by rebels as recently as Saturday, pushing them back towards last bastion of control on the west bank of Aleppo's river.

The Syrian army is backed by Russian war planes and Shi'ite militias supported by Iran.

A correspondent for Syria's official SANA news agency said the army had taken control of Sheikh Saeed, and more than 3,500 people left at dawn.

A Syrian official told Reuters: "We managed to take full control of the Sheikh Saeed district. This area is very important because it facilitates access to al-Amariya and allows us to secure a greater part of the Aleppo-Ramousah road." The road is the main entry point to the city from the south.

Civilians

The Russian Defence Ministry said on Monday that 728 Syrian rebels had laid down their weapons over the previous 24 hours and relocated to western Aleppo.

The Defence Ministry also said that 13,346 civilians left rebel-controlled districts of Aleppo over the same period.

The Observatory said that four weeks into the army offensive at least 415 civilians, including 47 children, had been killed in rebel-held parts of the city.

It had documented hundreds of injuries as a result of Russian and Syrian air strikes and shelling by government forces and its allies on the besieged eastern part of the city.

The Observatory said 364 rebel fighters had been killed in the eastern sector. It said rebel shelling of government-held west Aleppo had killed 130 civilians, including 40 children. Dozens had been injured.

The army on Sunday took foreign journalists to witness an enlistment ceremony for 220 men, including former rebels and others from opposition-held areas captured by the government.

The fate of young men leaving the shrinking rebel pocket in Aleppo has been a subject of argument between the two sides.

Opposition supporters have accused the government of mass arrests and extrajudicial killings, which Damascus has denied. The government accuses rebels of forcing people in their areas to fight for them and preventing them leaving, which the insurgents deny.

The United Nations said last week it was concerned about reports that hundreds of young men had been detained upon leaving the rebel-held enclave as it collapsed in the face of a Syrian army advance.