Moscow announced a "humanitarian pause" and halted air raids last week to allow rebels and civilians to flee Aleppo. Since 2012, Aleppo has been divided between opposition districts in the east and government-controlled neighbourhoods in the west.
Since Sunday, rebel forces have warned residents in the east to avoid front-line areas, apparently in anticipation of more attacks, including those by pro-government militiamen from countries such as Iran, Lebanon and Iraq.
Before the pause, Russian and Syrian government warplanes had been targeting homes, hospitals and infrastructure in the city's east.
Russia recently signalled a major escalation in Syria, apparently dispatching warships, including an aircraft carrier that can hold as many as 40 planes. A spokesman for Russian President Vladimir Putin, Dmitry Peskov, upped the ante by vowing that all of Syria had to be "liberated" by Assad's forces.
Aleppo has become a key battleground in the conflict, which began in 2011 and has killed more than 400,000 people. Seizing the eastern districts of Aleppo - Syria's commercial hub before the war - would mark a major victory for Assad.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said on Sunday that more than 2100 civilians, including 479 children, have been killed in Aleppo in the past six months.