Opposition fighters have advanced in and around Syria’s second-largest city, and also claim to be in control of all of Idlib province.
Russian and Syrian jets have responded by bombing the rebels as they contend with the most serious challenge to President Bashar al Assad in many years.
Syria’s military says it has conducted a “temporary troop withdrawal” to prepare for a counteroffensive against “terrorists”.
Aleppo airport and a number of major roads have been closed, while thousands of cars were seen fleeing the city along a route that remains under government control.
The rebels, led by the Islamist militant group Hayat Tahrir al Sham, are said to be in control of around half of Aleppo, according to the UK-based Syrian Observatory for Human Rights (SOHR).
Dozens of Syrian soldiers have been killed in fierce battles in Aleppo and Idlib in the past few days, the military has said.
Russia, one of President Bashar al Assad’s key allies, has promised Damascus extra military aid to thwart the rebels, two military sources told the Reuters news agency.
The sources added that the Syrian army had been told to follow “safe withdrawal” orders from the main areas of the city that the rebels have entered.
“Relentless attacks” over the past three days in northwestern Syria have killed 27 civilians, including eight children, a UN official said.
And they have now returned to Aleppo for the first time since 2016, when Assad and his allies Russia, Iran, and regional Shia militias retook it.
The opposition fighters have said the campaign is in response to stepped-up strikes in recent weeks against civilians by the Russian and Syrian air forces on areas in rebel-held Idlib.
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Opposition sources in touch with Turkish intelligence said Turkey, which supports the rebels, had given a green light to the attacks.
However, Turkish foreign ministry spokesperson Oncu Keceli said on Friday that Turkey sought to avoid greater instability in the region and had warned recent attacks undermined de-escalation agreements.
The Russian and Turkish foreign ministers have discussed the situation on the phone and expressed concerns over escalation, according to Moscow.
Insurgents have posted videos online showing themselves using drones in their advance for the first time. It is not clear to what extent they were used on the battlefield.
Videos geolocated by Sky News show armoured vehicles on the fringes of Aleppo and rebels celebrating at its western entrance.
Another shows a group of more than 10 men running through the streets. At least one of them appears to be armed.
The Syrian government has not commented on the rebels breaching the city limits.
