REUTERS/Medecins Sans Frontieres
The bombing continued for 30 minutes after staff raised the alarm to U.S. and Afghan military officials, the aid group said.
At least 37 people were wounded and many are still missing after the bombing, which will renew concerns over the use of U.S. air power in the conflict in America's longest war. Former President Hamid Karzai fell out with his backers in Washington over the number of civilians killed by bombs.
U.S. forces launched an air strike at 2.15 a.m. (2145 GMT), the spokesman, Col. Brian Tribus, said in a statement.
"The strike may have resulted in collateral damage to a nearby medical facility," he added. "This incident is under investigation."
At the aid group's bombed-out hospital, one wall of a building had collapsed, scattering fragments of glass and wooden door frames, and three rooms were ablaze, said Saad Mukhtar, director of public health in Kunduz.
"Thick black smoke could be seen rising from some of the rooms," Mukhtar said after a visit to the hospital. "The fighting is still going on, so we had to leave."
Fighting has raged around the northern provincial capital of Kunduz as government forces backed by American air power seek to drive out Taliban militants who seized the city six days ago in the biggest victory of their nearly 14-year insurgency.
The U.S. military unleashed twelve air strikes on the city this week, most on the city's outskirts. The overnight strike on the hospital was only the second in a central area, the military said.
Despite government claims to have taken control of the area, a bitter contest with the Taliban continues. Afghan security forces fought their way into Kunduz three days ago, but battles continue in many places, with Taliban hiding in people's homes.
"Tragic Incident"
Many patients and staff remain missing after the attack which happened when almost 200 patients and employees were in the hospital, the only one in the region that can deal with major injuries, said Medecins Sans Frontieres, which is based in Switzerland.
"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.
MSF said it gave the location of the hospital to both Afghan and U.S. sides several times in the past few months, as well as this week, to avoid being caught in crossfire.
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Taliban spokesman Zabihullah Mujahid said there were no militant fighters being treated at the hospital.
MSF said it had treated almost 400 patients in the 150-bed hospital since fighting broke out, most for gunshot wounds. So many patients have flooded in that the hospital had to put them in offices and on mattresses on the floor. The U.S. embassy in Kabul said in a statement it "mourns for the individuals and families affected by the tragic incident".
The hospital was on the frontline in the fighting. On Friday, Taliban fighters hiding behind the walls of the hospital were firing at government forces, said Khodaidad, a Kunduz resident who lives near the hospital.
REUTERS/Medecins Sans Frontieres
EU Commissioner for Crisis Management Christos Stylianides said he was shocked by the news of the bombing.
"I call on all parties to the conflict to respect international humanitarian law and ensure that health care facilities and humanitarian workers are protected," he said in a statement.
France has called for an investigation.
The International Committee of the Red Cross said it was "deeply shocked" by the incident.
"This is an appalling tragedy," said Jean-Nicolas Marti, head of the ICRC in Afghanistan. "Such attacks undermine the capacity of humanitarian organizations to assist the Afghan people at a time when they most urgently need it."