The shooting at the airport came as the Taliban sent fighters north of the capital to eliminate pockets of armed resistance to their lightning takeover earlier this month.
Potential Islamic State threats against Americans in Afghanistan are forcing the U.S. military to develop new ways to get evacuees to the airport in Kabul.
The insurgents have taken 18 of the country’s 34 provincial capitals in recent days, including its second- and third-largest cities, Herat and Kandahar.
Kunduz is one of the country’s larger cities with a population of more than 340,000, and was a key area defended against Taliban takeover by Western troops over the years.
U.S. Defense Secretary Lloyd Austin arrived Sunday in Kabul on his first trip to Afghanistan as Pentagon chief, amid swirling questions about how long American troops will remain in the country.
The report comes as the Biden administration plans to take a new look at the peace agreement between the U.S. and the Taliban signed last February under President Donald Trump.