KABUL (Reuters) - Medical aid group Medecins Sans Frontieres (MSF) on Sunday demanded an independent international inquiry into a suspected U.S. air strike that killed 22 people in an Afghan hospital it runs, branding the attack a “war crime”.

U.S. Defense Secretary Ash Carter promised a full investigation into whether the American military was connected to the destruction of the hospital, but cautioned it would take time to gather information.

“We do know that American air assets ... were engaged in the Kunduz vicinity, and we do know that the structures that - you see in the news - were destroyed,” Carter told reporters traveling with him shortly before landing in Spain on Sunday. “I just can’t tell you what the connection is at this time.”

The Pentagon chief would not speculate on what occurred but said Washington would hold accountable “anybody responsible for doing something they shouldn’t have done.”

MSF said a U.S. military probe into the incident, which occurred during a push by Afghan security forces to retake the key northern city of Kunduz from Taliban insurgents, was not enough.

“Relying only on an internal investigation by a party to the conflict would be wholly insufficient,” MSF General Director Christopher Stokes said in a statement.

“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,” Stokes said.

Battles were still raging on Sunday around Kunduz, a city of 300,000, as government forces backed by U.S. air power sought to drive out the Taliban militants who seized the city almost a week ago in one of their biggest victories in the 14-year war.

Decomposing bodies littered the streets and trapped residents said food was becoming scarce.

“This city is no longer fit for living,” said the province’s public health director, Sayed Mukhtar.

Any confirmation of U.S. responsibility for the hospital deaths would deal a blow to Afghan President Ashraf Ghani’s policy of forging closer ties with the United States. His predecessor, Hamid Karzai, fell out with his backers in Washington in part over the number of civilians killed by U.S. strikes.

But the Afghan leader will be torn between distancing himself from Washington and the need for American firepower to help his forces drive insurgents out of Kunduz.

The U.S. military said it conducted an air strike “in the vicinity” of the MSF hospital as it targeted Taliban insurgents who were directly firing on U.S. military personnel. It has not acknowledged hitting the hospital.

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U.S. officials, speaking on condition of anonymity, said a U.S. military AC-130 gunship had been operating in the area, firing at Taliban targets after receiving a request for support from U.S. special operations forces advising Afghan troops.

President Barack Obama offered condolences on Saturday to the victims of what he called “the tragic incident”. The U.N. human rights chief called the hospital assault “inexcusable” and also said it could amount to a war crime.

The U.S.-led coalition force in Afghanistan said it expected to complete its preliminary multinational investigation within days.

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STAFF PULLED OUT

In Kabul, the Ministry of Defence said Taliban fighters had attacked the hospital and were using the building “as a human shield”.

But MSF denied that, saying it was “disgusted by the recent statements coming from some Afghanistan government authorities justifying the attack” on its hospital in Kunduz.

“These statements imply that Afghan and U.S. forces

working together decided to raze to the ground a fully functioning hospital – with more than 180 staff and patients inside – because they claim that members of the Taliban were present. This amounts to an admission of a war crime,” Stokes said in a later statement.

In the air strike, witnesses said patients were burned alive in the crowded hospital. Among the dead were three children being treated.

MSF said on Sunday it had pulled most of its staff out of the area because the hospital that was a lifeline for thousands in the city was no longer functioning. Some staff had gone to help treat the wounded at other hospitals outside of Kunduz.Earlier this year, an Afghan special forces raid in search of a suspected al Qaeda operative prompted the hospital to temporarily close to new patients after the soldiers were accused of behaving violently towards staff. The struggle to retake Kunduz has raised questions over whether NATO-trained Afghan forces are ready to go it alone now that most foreign combat troops have left. Afghan security forces conducted house-to-house searches in Kunduz on Sunday as gunbattles 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 past week.