A police spokesperson told Efe news a group of Taliban militants attacked security checkposts in Dasht-e-Archi district on Tuesday night.
He said that security forces, most of them members of the Afghan National Army, suffered casualties.
But Safiullah Amiri, deputy head of Kunduz provincial council, said 13 members of the security forces were killed.
"Twelve of them (were) members of the army and one of them a policeman," Amiri told Efe news, adding 12 security personnel, including eight soldiers, were injured in the attack.
Another provincial administration official said three members of the army were missing after the gunfight that lasted for several hours.
"Taliban also suffered casualties in this attack but their number is not yet clear," he told Efe news.
Taliban spokesperson Zabihullah Mujahid in a statement claimed responsibility, saying 35 soldiers were killed and four were captured during the attack.
Mujahid said four armoured vehicles of the security forces were destroyed and Taliban fighters seized dozens of weapons as well after the gunfight.
The attack came a day after the Taliban claimed on Monday that they shot down a US plane in Ghazni province.
The US forces on Tuesday recovered two bodies from the site of the military plane crash.
( With inputs from IANS )