An Afghan Defence Ministry statement says "Fresh troops have arrived in Kunduz and an operation has been launched."
The Taliban had seized Kunduz, taking control of most areas and freeing hundreds of prisoners from jail.
Hundreds of militants stormed the city before dawn, quickly seizing key buildings and advancing on the airport.
After storming the city of Kunduz, one of the Taliban's first acts was to free prisoners.
At worst they'll join the Taliban ranks ... at best they'll be criminals on the loose.
Reinforcements are on the way to the Afghan Army, but in the meantime Commander General Muran Ali Murad is offering a positive take on their retreat.
"The reason we have stepped back from the city is because of civilian casualties. We have tried to avoid the destruction of shops and businesses and homes. Without the free movement of our security forces in the city, we are avoiding civilian casualties."
The Afghan interior ministry's confirmed "most of Kunduz city" is under Taliban control.
Former Kunduz member of Parliament, Moein Marastial, says people are scared.
"People are all afraid. They are all in their houses - nobody is in the streets or in the city. They are worried about the attacks."
But to some residents the Taliban fighters seem most welcome.
(resident): "Did you take over the area?"
(fighter) "God willing... This is our hope. We want to build a religious school, to build a school, to build a bridge, a road, a Sharia-based government. This is why we came out and this is what we fought for - so that Sharia law is in force here."
(resident): "God willing. God willing."
Despite losing about 25 men, the Taliban is calling its Kunduz operation "an immense conquest".
Conquest or not, the Afghan Security Force's General Ahmad Khan Habibi admits the army was caught off-guard.
"The enemy again used a local house as shelter and started their terrorist attacks. They have been defeated in most locations, we will chase them and be sure that they will be defeated."
If they keep it, Kunduz would be the first provincial capital taken by the Taliban since they lost power in 2001's US-led invasion.
Kunduz Police chief, Qasim Jangal Bagh, says they may be fighting alone since the army withdrew but they'll fight to the end.
"All of our Afghan forces are fighting the enemies and until the last drop of our blood we will defend this territory and be confident they are not able to do anything."
But General Muran Ali Murad says it appears the Taliban is getting help from battle-hardened fighters, maybe from Syria and Iraq.
"Today's incident in Kunduz was a terrorist act by certain groups. The attack was launched by different groups of local and foreign terrorists with support from their foreign networks. And thanks to their foreign support, they managed to enter the city."
Kunduz is a key strategic transport hub.
Losing it would be a disaster for Afghanistan's unity government, which is marking its first anniversary today.
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