A hospital, blood bank and ambulances are reported to have been hit as Syrian government aircraft and artillery bombarded rebel-held eastern Aleppo.
The director of the Bayan Children's Hospital said he was sheltering in the facility's basement, unable to leave.
The UK-based Syrian Observatory for Human Rights said at least 21 people had been killed, five of them children.
The air strikes resumed on Tuesday after a three-week moratorium declared by the government's ally Russia ended.
Russia also announced the start of a major operation against jihadist militants elsewhere in western Syria that saw the country's only aircraft carrier used in combat for the first time.
Aleppo, once Syria's commercial and industrial hub, has been divided in roughly two since 2012, with the government controlling the west and rebels the east.
In the past year, Syrian troops have broken the deadlock with the help of Iranian-backed militias and Russian air strikes.
On 22 September, two weeks after encircling the east and imposing a siege on its 275,000 residents, they launched an all-out offensive to take full control of the city.
The government and its ally Russia halted air strikes on 18 October to allow civilians and rebels to leave, but few took up the offer.
By the end of the month, air strikes and shelling had killed more than 700 civilians in the east, while rocket-fire had left scores dead in the west, according to the UN.
On Tuesday, activists said the government's air strikes had resumed, killing at least 11 people, amid reports by state media of large troop deployments on several fronts ahead of a major ground assault.
The Syrian Observatory, a monitoring group, said missiles fired by jets, barrel bombs dropped from helicopters and artillery targeted several areas on Wednesday, including Shaar, Sukkari, Sakhour and Karam al-Beik.
The Independent Doctors Association, which supports several facilities in Syria, reported that the Bayan Children's Hospital had been badly damaged.
It quoted the hospital's director, Dr Hatem, as saying he was trapped in the basement. "The planes are up above. We can't get out. Maybe we can protect ourselves in this room," he added.
Rescue workers from the Syria Civil Defence, who are also known as the White Helmets, meanwhile said that a paramedic had been killed in Karam al-Beik.
"The helicopters won't stop for a single moment," spokesman Bebars Mishal told the Reuters news agency. "Right now, the bombing won't let up."
Air raids also reportedly continued in the countryside west of Aleppo. The Syrian Observatory said at least 19 people were killed in the village of Batbo.