Medical charity Doctors Without Borders says it has withdrawn staff from the embattled Afghan city of Kunduz, a day after an apparent US bombing raid on its hospital which the UN says could amount to a war crime.

The charity, which goes by its French initials of MSF, said on Sunday at least 19 people were killed in the attack, some of whom burned to death in their beds as the bombardment continued for more than an hour. The strikes continued even after US and Afghan authorities were informed the hospital had been hit.

It is the only medical facility in the whole northeastern region of Afghanistan that can deal with major war injuries. Its closure, even temporarily, could have a devastating impact on local civilians.

"The MSF hospital is not functional anymore. All critical patients have been referred to other health facilities and no MSF staff are working in our hospital," Kate Stegeman, a spokeswoman for the charity, told AFP on Sunday.

"I can't confirm at this stage whether our Kunduz trauma centre will reopen or not."

The air raid came five days after Taliban fighters seized control of the strategic northern city of Kunduz, in their most spectacular victory since being toppled from power by a US-led coalition in 2001.

The medical charity condemned the bombings as "abhorrent and a grave violation of international law", demanding answers from US-led NATO forces in Afghanistan.

It said Afghan and coalition troops were fully aware of the exact location of the hospital, having been given GPS co-ordinates of a facility which had been providing care for four years.

It added that despite frantic calls to military officials in Kabul and Washington, the main building housing the intensive care unit and emergency rooms was "repeatedly, very precisely" hit almost every 15 minutes for more than an hour.

MSF said some 105 patients and their caregivers, as well as more than 80 international and local MSF staff, were in the hospital at the time of the bombing.

"The bombs hit and then we heard the plane circle round," said Heman Nagarathnam, MSF's head of program in northern Afghanistan.

"There was a pause, and then more bombs hit. This happened again and again. When I made it out from the office, the main hospital building was engulfed in flames.

"Those people that could had moved quickly to the building's two bunkers to seek safety. But patients who were unable to escape burned to death as they lay in their beds."

At least 12 staff members and seven patients, among them three children, were killed, while 37 people were injured.

US President Barack Obama offered his "deepest condolences" for what he called a "tragic incident".

"The Department of Defense has launched a full investigation, and we will await the results of that inquiry before making a definitive judgment as to the circumstances of this tragedy," Obama said.

NATO earlier conceded US forces may have been behind the bombing, after its forces launched a strike which they said was intended to target militants.