Sayed Sarwar Hussaini, the spokesman for the provincial police chief, said the insurgents overran more than half the city after launching coordinated early morning attacks.
The buildings taken include a hospital, a courthouse and other government buildings.
The city’s fall would mark a major loss for the government as it struggles to combat the insurgents without the aid of US and Nato combat troops. Interior Ministry spokesman Sediq Sediqqi said the target of the assault was the city’s main prison and police headquarters.
He said security forces in Kunduz, which managed to fend off a major Taleban advance earlier this year, had intelligence that another attack was being planned.
“Security forces in Kunduz were prepared for an attack but not one of this size, and not one that was coordinated in ten different locations at the same time,” he said.
“Right now intensive gun battles are going on inside the city. Part of the city is under the control of the Taleban, including the markets, shops and a number of government buildings.”
The strategically located Kunduz, capital of the province of the same name, is one of Afghanistan’s wealthiest cities. The “breadbasket” province is a major producer of grain and other food.
The Taleban launched their spring offensive with a major attack on Kunduz in April. They were pushed back by Afghan security forces but are believed to have regrouped and allied with other insurgents.
Hundreds of gunmen stormed the city at around 3am yesterday, from several directions, officials said.
Kunduz governor Omar Safi was not in the city at the time, they added. The United Nation’s Assistance Mission to Afghanistan said all its staff had been evacuated from its Kunduz office.
On his Twitter account, Taleban spokesman Zabihullah Mujahid claimed responsibility for the attack, saying the fighters were entering hospitals around the city hunting for wounded government troops.
He advised residents to remain indoors.
Abdul Wadood Wahidi, spokesman for the Kunduz governor, said earlier that three police officers had been wounded and “more than 20 bodies of Taleban fighters are on the battlefield”.
He said reinforcements from neighbouring provinces had already arrived in Kunduz city.