A suspected US air strike on a charity hospital in the Afghan city of Kunduz killed 19 people Saturday, a bombardment US President Barack Obama said was a "tragic incident" but which the UN condemned as "inexcusable".

Washington has promised a "full investigation" into the bombing at the facility, a key lifeline that has been running beyond capacity during fighting that saw the Taliban seize control of the northern provincial capital for several days.

The attack early Saturday left the building engulfed in flames, and dozens more people seriously wounded, with photos posted by Doctors Without Borders (MSF) showing their staff shocked and dazed.

"At 2:10 am (2040 GMT) local time... the MSF trauma centre in Kunduz was hit several times during sustained bombing and was very badly damaged," the organisation, known by its French initials, said.

"Twelve staff members and at least seven patients, including three children, were killed; 37 people were injured. This attack constitutes a grave violation of international humanitarian law."

The charity said the bombing continued for more than 30 minutes after American and Afghan military officials were first alerted they were being hit.

"All parties to the conflict, including in Kabul and Washington, were clearly informed of the precise location (GPS coordinates) of the MSF facilities," the statement added.

MSF said the aerial raid hit the main hospital building housing the intensive care unit and emergency rooms, while the surrounding buildings were left untouched.

- 'Collateral damage' -

NATO conceded US forces may have been behind the strike on MSF, which has long treated the war-wounded from all sides of the conflict.

"The strike may have resulted in collateral damage to a nearby medical facility. This incident is under investigation," a NATO statement said.

The incident has renewed concerns about the use of US air strikes in Afghanistan, a deeply contentious issue in the 14-year campaign against Taliban insurgents.

UN rights chief Zeid Ra'ad Al Hussein called for a full and transparent probe, noting that, "an air strike on a hospital may amount to a war crime".

"This event is utterly tragic, inexcusable and possibly even criminal," he said.

Obama offered his "deepest condolences" for the "tragic incident" and said the Pentagon would carry out a full investigation.

US Defense Secretary Ashton Carter said that "US forces in support of Afghan Security Forces were operating nearby, as were Taliban fighters".

The Pentagon gave no further details, but one US official said the investigation will focus on the role played by a US AC-130 gunship.

The bombing came after Taliban insurgents overran the northern Afghan city on Monday. It was the first major city to be captured by militants since 2001.

The Afghan defence ministry expressed sadness but in a statement said "a group of armed terrorists... were using the hospital building as a position to target Afghan forces and civilians".

- 'Again and again' -

MSF said some 105 patients and their caregivers, as well as more than 80 international and local MSF staff, were in the hospital, the only medical facility in the area that can deal with major injuries, at the time of the bombing.

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

"There was a pause, and then more bombs hit. This happened again and again. 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."

The soot-blackened building was filled with the smell of burning flesh and some bodies were charred beyond recognition, said Qiamudeen, a 31-year-old shopkeeper whose neighbour was killed in the strike.

"I was shocked, emotional and in tears when I reached the hospital," Qiamudeen, who goes by one name, told AFP.

Though the Afghan government insists the city is firmly in their control, many Kunduz residents were too afraid to leave their homes to check on wounded relatives because of sporadic firefights between troops and Taliban snipers lurking in the city.

Kunduz is facing a humanitarian crisis, with thousands of civilians caught in the crossfire between government forces and insurgents. At least 60 people are known to have died and 400 wounded in recent fighting.

The Taliban's offensive in Kunduz, their biggest tactical success since 2001, marks a major blow for Afghanistan's Western-trained forces.

US-led NATO forces ended their combat mission in Afghanistan last December, though a 13,000-strong force remains for training and counter-terrorism operations.