The US has vowed to fully investigate claims its forces are responsible for an air strike on a hospital in Afghanistan that killed 19 people.

US President Barack Obama has offered his condolences over the suspected US airstrike on a hospital in the city of Kunduz.

He said the Department of Defence has launched an investigation.

Dozens more people were wounded at the hospital which had been a key lifeline during fighting in the city which saw the Taliban take control for several days last week.

The medical charity Doctors Without Borders has accused US forces of continuing to bomb its facility in Kunduz for more than half an hour after it had informed Washington of its location.

The hospital had been serving as a vital lifeline during fighting last week which at one point saw the city fall under the control of the Taliban for several days.

The US is promising a "full investigation" into the deadly bombing.

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

12 staff from the Doctors Without Borders charity were among the dead, known by its French acronym MSF.

Dozens more were seriously wounded 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.

"A full investigation into the tragic incident is under way in coordination with the Afghan government," Carter said in a statement.

He added that the United States would "continue to work with our Afghan partners to try and end the ongoing violence in and around Kunduz."

The strike early on Saturday left the building engulfed in flames, with photos posted by MSF showing its staff shocked and dazed.

The charity said the bombing continued for more than 30 minutes after US and Afghan military officials were first alerted that the hospital was being hit.

NATO conceded that US forces may have been behind the strike but has not so far commented on the specific claims of MSF, which has long treated the war-wounded from all sides of the conflict.