Fighting around Imam Sahib district began late on Sunday and by mid-day on Monday the Taliban had overrun the district headquarters and were in control of police headquarters, provincial police spokesman Inamuddin Rahmani said.

Taliban militants were within one kilometre of Kunduz, the provincial capital, but had not entered into the city, he said, although there were reports of small bands of Taliban near the outskirts and residents trying to leave for Kabul.

Dozens of districts have fallen to the Taliban since May 1, when Australian and NATO troops began their final departure from Afghanistan.

Imam Sahib is strategically located near Afghanistan's northern border with Tajikistan, a key supply route from Central Asia.

Rahmani said police and Afghan National Army soldiers had jointly tried to defend the district and it was still not clear how many casualties were suffered in the protracted battle or how many Taliban were killed or wounded.

Taliban spokesman Zabihullah Mujahed confirmed Imam Sahib district was in the group's hands.

Several other districts in Kunduz have also fallen in the latest round of fighting, including Dasht-e-Archi, which neighbours Imam Sahib, Rahmani said, further consolidating local transportation links in the area.

In recent days, the Taliban have taken several districts across the three northern provinces of Kunduz, Baghlan and Balkh.

Significantly, witnesses said Doshi district in Baghlan province was in Taliban hands, which if true gives the insurgent group control of the one road that links five northern provinces to the capital Kabul.

On Sunday, Taliban leader Mawlawi Hibatullah Akhunzada issued a statement ordering his soldiers to "treat those who surrender well and display good behaviour with them".

Taliban gains and the steady withdrawal of the remaining 2500-3500 US troops and 7000 NATO forces have lent an urgency to efforts to find a negotiated end to Afghanistan's protracted conflict.

Talks between the government and the Taliban taking place in Qatar have reached a stalemate.

While Taliban leaders say they are ready to negotiate, observers familiar with the talks say the insurgent movement seems more anxious to chalk up military gains hoping to strengthen their negotiating position.

Meanwhile, the White House on Sunday announced President Joe Biden will meet on Friday in Washington with Afghan President Ashraf Ghani and Abdullah Abdullah, the head of the country's High Council for National Reconciliation, which overseas the government's negotiation team.

Australian Associated Press