Air strikes on a children's hospital and two others in the divided Syrian city of Aleppo sparked a desperate bid by medical staff to rescue at least nine newborns.

The UN's children's agency UNICEF and doctors at Al-Hakim children's hospital said Wednesday's attacks in the rebel-controlled part of the city were chilling.

The attacks happened within three hours and also targeted the nearby Al-Bayan hospital away and the Abdulhadi Fares Clinic, the agency said in a statement.

"On Wednesday morning, the hospital was the target of an aerial raid and a barrel bomb fell near here. Thank God, there was only material damage," Riyadh Najjah, a doctor at the hospital, told AFP.

"Doors and windows and a few incubators were broken. That's why we had to bring the children to a safer place. Now, we are fixing the damage, and soon we will resume work," he added.

A leading paediatrician described the aftermath of the raid in statements to the Syria Campaign advocacy group.

"It was a horrible moment. The nurses were trampling each other to rush the babies to the basement, while many of them started to cry," said doctor Hatem, whose full name was not disclosed.

The nurses were worried the newborns would breathe in the dust and debris in the wake of the raid, he said.

"We expected that it would happen one day, and today is that day. There are now only 18 incubators left in eastern Aleppo."

The newborns all survived, said an AFP correspondent who toured Al-Hakim on Thursday.

He counted 10 newborns, some of them placed in the basement of the building.

While some cried others were fed with a bottle. Nurses were also regularly monitoring their heart rates on screens.

"Al-Hakim hospital, a UNICEF supported facility, is one of the few that still provides paediatric services. This is the second attack on the hospital," the UN children's agency said.

"Everyone must question their humanity when babies have to be taken out of incubators because of attacks on hospitals," said Peter Salama, its regional director for the Middle East and North Africa.

- 'Running out of options' -

The Syrian Observatory for Human Rights said 15 people were killed in the attacks, most of them when the barrel bomb -- a crude and unguided explosive device -- was dropped on the area.

Aleppo was once Syria's commercial powerhouse, but it has been a battleground since 2012 when rebels seized the east of the city confining the army to the west.

Since then, the rebels have repeatedly pounded government-held areas with rocket and mortar fire, while the army has hit rebel neighbourhoods with air strikes.

Founded in mid-2012, Al-Hakim hospital has been forced to relocate multiple times in fear of government raids, said its funder, the Independent Doctors Association.

Syria's devastating conflict has killed more than 280,000 people and has seen hospitals destroyed across the country.

In April, doctor Hatem mourned the death of his colleague Mohammad Wassim Maaz, killed in an air strike at Aleppo's Al-Quds hospital which also claimed the lives of a dentist, three nurses and 22 civilians.

"I want every president to imagine that one of these newborns were his own son or daughter. Whatever they would do for their sons if they were bombed, they must do for these newborns."

Doctors in opposition-controlled parts of Aleppo city have raised alarm over medical conditions there, particularly as the last route out into the rest of the province is under near-daily bombardment.

"Aleppans' options are running out," said doctor Samah Bassas of the Syria Relief Network, an umbrella organisation of 60 humanitarian groups in Syria.

"The bombs we are used to. But if we are to be held under siege, hunger and disease will quickly take hold. Even more death is inevitable," she said.