A US air strike may have hit a hospital run by Medecins Sans Frontieres (MSF), a NATO forces spokesman said, after the medical aid group blamed an aerial attack for the destruction in the northern Afghan city of Kunduz that killed three staff.

Fighting has raged around the Afghan provincial capital, recaptured by government forces this week from Taliban militants who had seized it in the biggest victory of their nearly 14-year insurgency.

US forces launched an air strike in the city at 2:15 am (5.45 pm EDT Friday), the spokesman, Col. Brian Tribus, said in a statement on Saturday.

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

MSF said 30 of its staff were still missing after the partial destruction of its trauma center, hit several times in sustained bombing that the group called an "aerial attack".

"We are deeply shocked by the attack, the killing of our staff and patients and the heavy toll it has inflicted on healthcare in Kunduz," the aid group's operations director, Bart Janssens, said in a statement.

Taliban spokesman Zabihullah Mujahid said U.S. air strikes targeted the hospital and had killed patients, doctors and nurses. None of its fighters was a patient in the hospital at the time of the attack, the militant group said.

The US military has unleashed several air strikes this week in support of government forces in the city, where Taliban fighters were still holding out against Afghan troops on Friday.

MSF said it did not have full casualty figures from the attack and its staff were treating injured patients and employees.