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KABUL — A medical aid group on Sunday struck back at allegations that Taliban fighters were operating in an Afghan hospital that was bombarded by U.S. forces, leaving at least 22 dead on Saturday.

"We reject reports that any Taliban were inside the hospital at the time of bombing or if any shots were fired," Kate Stegeman, communications manager for Doctors Without Borders (Medecins Sans Frontieres / MSF) in Kabul told NBC News.

The hospital was hit by a coalition airstrike on 2:15 a.m. local time on Saturday (5:45 p.m. ET Friday).

"There were 105 patients and about 80 MSF staff at the hospital at the time of bombing and as we said earlier 12 dead MSF staff are confirmed dead and 19 injured. Ten patients including three children were also killed and 18 others including caretakers were injured," Stegeman said.

"Bombing a fully functioning hospital can never be justified."

The Afghan Ministry of Defense earlier Sunday had said Taliban fighters had attacked the hospital and were using the building "as a human shield."

And a senior Afghan commander who didn't want to be named further told NBC News Sunday that alarge group of Taliban had taken position inside the hospital which was bombed by coalition forces, at least 15 enemy were killed in the hospital."

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But in a statement Sunday, MSF noted that "The gates of the hospital compound were closed all night so no one that is not staff, a patient or a caretaker was inside the hospital when the bombing happened."

And, the group noted, "in any case, bombing a fully functioning hospital can never be justified."

President Barack Obama said the U.S. Department of Defense had ordered a full investigation into the incident as the U.N. human rights chief said the assault on the hospital was "utterly tragic, inexcusable" and could amount to a war crime.

In a statement, Obama also offered condolences to the victims of what he called "the tragic incident."

MSF also rejected the notion that the U.S. could investigate itself.

“Under the clear presumption that a war crime has been committed, MSF demands that a full and transparent investigation into the event be conducted by an independent international body," the group said. "Relying only on an internal investigation by a party to the conflict would be wholly insufficient. Not a single member of our staff reported any fighting inside the MSF hospital compound prior to the U.S. airstrike on Saturday morning."

Meanwhile, fighting raged around the northern provincial capital of Kunduz for a seventh day as government forces backed by American air power seek to drive out Taliban militants who seized the city almost a week ago.

Fires burn in part of the hospital run by Doctors Without Borders (MSF) in the Afghan city of Kunduz after it was hit by an air strike. MSF / AFP - Getty Images

The struggle to retake Kunduz has raised questions over whether NATO-trained Afghan forces were ready to go it alone now that most foreign combat troops have left. Afghan security forces were conducting house-to-house searches on Sunday, as gun battles persisted in parts of the city, said Hamdullah Danishi, acting governor of Kunduz province. He said 480 Taliban fighters and 35 soldiers had been killed.

The army raised the national flag in the central square, an area of the city that has changed hands several times in the fighting during the last week. "Our security forces took control of strategic areas in Kunduz," Danishi said. "We have a clearance operation ongoing."

Afghan military helicopters on Sunday dropped 6,000 leaflets urging people to cooperate with the army, the defense ministry said. "If you see abandoned military vehicles or equipment anywhere turn them over to security forces," the leaflets read. Corpses lay in the streets and people were too afraid to leave their homes, said one resident, Gulboddin.

"You can hear the sound of gunfire all over the city," said Gulboddin, who has only one name. "Some of the bodies are decomposing."