Officials said they were in control of the northern provincial capital while in the east of the country, a US military transport plane crashed killing 11 people including six US soldiers.
The Taliban claimed to have shot the C-130 Hercules down near Jalalabad. However, US Major Tony Wickman told AFP: "With a high degree of confidence I can say that an enemy attack did not contribute to the crash. It is under investigation."
Officials said today that Afghan forces had secured the city after days of fierce clashes with the insurgents clouded by confusing and contradictory claims by the government and the Taliban over who was in control.
"Today our security forces are deployed all over Kunduz," provincial police spokesman Sayed Sarwar Hussaini told AFP. "We are searching the lanes of the city and residential houses looking for Taliban militants... We will target and kill them."
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Residents told AFP this morning that the fighting appeared to have ceased.
"You don't see anyone in the streets, the shops are closed, and there is no fighting between the Taliban and government forces," Zabihullah, a Kunduz resident who goes by one name, told AFP.
Some people injured during the fighting were too afraid of Taliban attack to leave their homes and go to hospital, he said, adding that food was running short and there was no electricity.
Shahir, another resident who goes by one name, said that sounds of gunfire or explosions in the city had become more intermittent by this morning.
Late yesterday, residents had said fierce gun battles and explosions were still echoing in parts of the city, and the streets were littered with Taliban bodies and charred and mangled vehicles.