Air raids were halted on Thursday evening following Moscow's announcement but shelling continued throughout the night and into the morning, the Syrian Observatory for Human Rights said.
The sound of heavy artillery was heard throughout the night in the rebel-held enclave.
"There was heavy shelling of several besieged districts and fierce fighting, particularly in Bustan al-Qasr," one of the biggest districts still in rebel hands after the army's blistering three-week offensive, Observatory chief Rami Abdel Rahman told AFP.
After talks with US Secretary of State John Kerry in the German city of Hamburg on Thursday, Russian Foreign Minister Sergei Lavrov announced a pause in the army's assault to allow for the evacuation of some of the tens of thousands of civilians trapped in the now tiny rebel enclave.
Rebels are sceptical about the announcement due to previous annoucements by Russia of truces which have been quickly broken.
The army has recaptured 85 percent of the eastern sector of the city which the rebels had held since summer 2012.
"I can tell you that today combat operations by the Syrian army have been halted in eastern Aleppo because there is a large operation under way to evacuate civilians," Lavrov said. "There is going to be to a column of 8,000 evacuees."
In Washington, White House spokesman Josh Earnest said Lavrov's announcement was "an indication that something positive could happen".
The army's bombardment of rebel-held districts killed at least 18 civilians on Thursday, according to the Observatory, a Britain-based monitoring group which has a wide network of sources on the ground.