Afghan's president has appointed a team of investigators to look into the circumstances leading to the Taliban's brief capture of the northern city of Kunduz and US air strike that destroyed a hospital and killed at least 22 people.

Meanwhile, the Pentagon said it would offer "condolence payments" to civilians injured in the air strike and the families of those killed, as well as providing funds for repairing the hospital.

The compensation will be handled through the already existing Commanders' Emergency Response Programme in Afghanistan, and if necessary additional authority will be sought from Congress, Pentagon press secretary Peter Cook said.

The five-man delegation appointed by Ashraf Ghani will leave for Kunduz to conduct a province-wide probe into how the insurgents were able to overrun the city on September 28 and hold it for three days before government troops launched a counter-offensive.

Part of the team's mandate includes looking into the October 3 air strike on a trauma centre run by international charity Doctors Without Borders. The team will be led by the former head of the national intelligence agency, Amrullah Saleh, and reports to the president.

The "fact-finding team" will deliver a "comprehensive report so that we know what happened in Kunduz, what kind of reforms should be brought and what are the lessons learned for the future", the president said.

Government troops are still fighting to clear out pockets of Taliban insurgents, 10 days after entering Kunduz.

Sarwar Hussaini, a spokesman for the provincial police chief, said three areas had been retaken overnight, though a petrol station in Seh Darak was hit by a rocket and destroyed.

A Kunduz resident who would only give his first name, Abdullah, because of security concerns, said people were still leaving the city for safety and he had seen grocers emptying their shops of food to take home, fearing scarcities.

The World Food Programme said it was feeding thousands of people who had left Kunduz and were now living in camps in other cities in the north, and that "additional wheat is being milled in anticipation of increased needs in the coming days".

Food and water were still not getting through in adequate quantities, and the city remained without electricity, people said.

"The whole city is empty of people," Abdullah said. "Residents are still not feeling safe."

Representatives of Doctors Without Borders met Mr Ghani and his national security adviser Mohammad Hanif Atmar on Friday.

Mr Ghani told them he had ordered Afghan security forces to ensure the protection of humanitarian organisations. He said investigations were needed "so that we know what happened in the incident, how information was collected, and how the incident happened based on that information".

Doctors Without Borders has called for an independent probe of the incident by the Swiss-based International Humanitarian Fact-Finding Commission - made up of diplomats, legal experts, doctors and some former military officials from nine European countries, including Britain and Russia. It was created after the Gulf War in 1991 and has never deployed a fact-finding mission.

Doctors Without Borders, a Nobel Peace Prize-winning organisation that provides medical aid in conflict zones, is awaiting responses to letters sent on Tuesday to 76 countries that signed the additional protocol to the Geneva Conventions, asking to mobilise the 15-member commission.

For the IHFFC to be mobilised, a single country would have to call for the fact-finding mission and the US and Afghanistan - which are not signatories - must also give their consent.

The air strike was requested by Afghan ground forces, according to the commander of US forces in Afghanistan, General John Campbell, but mistakenly hit the hospital.

The bombing continued for about an hour and destroyed the hospital's main building. US president Barack Obama apologised and the American military is investigating. The hospital has been abandoned.

Doctors Without Borders said 12 staff members and 10 patients, all Afghans, were killed. Many more are still missing, though all foreign staff have been accounted for.