Afghan city of Kunduz overrun by Taliban
Hundreds of militants stormed the city before dawn, quickly seizing key buildings and advancing on the airport.
The government says it has sent reinforcements to Kunduz and fighting is ongoing.
Kunduz would be the first provincial capital taken by the Taliban since they lost power in 2001's US-led invasion.
The attack came a day before the first anniversary of President Ashraf Ghani's unity government.
Kunduz is strategically important as it acts as a transport hub for the north of the country.
It also has symbolic significance for the Taliban as it was their former northern stronghold before their government was overthrown.
"With the capturing of the police compound and governor's office in Kunduz, the whole province fell to our hands and our fighters are now advancing towards the airport," Taliban spokesman Zabihullah Mujahid said on his Twitter account.
A Taliban statement called the operation in Kunduz "an immense conquest" and urged its fighters to protect the local population.
The statement said the government in Kabul "should openly admit its defeat".
Earlier, the government admitted that it had lost control of parts of the city. It said at least 25 militants and two Afghan policemen had been killed and that reinforcements had been dispatched.