Six Afghan security forces were killed in the fighting over Darqad district, which borders Tajikistan, according to Sonatullah Taimor, the spokesman for the provincial governor.
The area was not affected by the earthquake that struck northern Afghanistan on Monday, with its epicenter in the neighbouring province of Badakhshan, he said.
The Taliban spokesman Zabihullah Mujahid emailed media organisations to say the battle for Darqad began at dawn today. Two Taliban fighters were killed, he said, as the insurgents captured government buildings, including police headquarters.
In late September, this combined force took control of the capital of northern Kunduz province, also called Kunduz, and held it for three days before Afghan forces launched a counteroffensive.
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The audacity of that attack took the Kabul government by surprise and highlighted weaknesses in intelligence and military organisation nine months after international combat forces led by the US withdrew from Afghanistan.
Some areas in Badakhshan that are suffering earthquake damage have a Taliban presence, officials have said, which could hamper relief efforts there.