Government strikes had halted briefly from last night, when Moscow announced a pause in the regime's offensive to allow the evacuation of civilians, though artillery fire did not stop.
Syria's army is three weeks into a battle to retake east Aleppo from rebels who are now confined to just a few neighbourhoods in their former bastion.
The city's loss would be the biggest blow for the rebels in the nearly six-year-old war, which has killed more than 300,000 people and displaced over half the country's population.
It also expressed concern about reports that hundreds of men had gone missing after fleeing to government-held territory.
The Syrian Observatory for Human Rights, a Britain-based monitor, reported at least a dozen air strikes on rebel-held neighbourhoods this afternoon.
Artillery fire had continued throughout last night and into today after Moscow's announcement, the monitor and an AFP correspondent reported.
Syria's army has captured around 85 per cent of east Aleppo, with rebels and remaining civilians confined to a shrinking space in increasingly grim conditions.
An AFP correspondent in east Aleppo said it had become increasingly difficult to find food because shopkeepers were too afraid to open and sell their meagre wares under the heavy government fire.
He said fleeing civilians had seen bodies lying uncollected in the streets of one neighbourhood because the intensity of the bombardment made it too dangerous to retrieve the dead.
Diplomatic efforts to reach a ceasefire have floundered, despite repeated discussions between Washington and Moscow, which back opposing sides in the conflict.
But Lavrov added military operations in the city would continue so long as rebels remained in Aleppo.
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