The Taliban says it has control of three-quarters of strategically valuable land near Kandahar, a city seen as the group's former stronghold.
The Taliban told Al Jazeera that it had been fighting international forces, and that a major battle was under way on Wednesday.
There had been 24 hours of heavy fighting.
A provincial police chief said that Afghan and Nato forces had killed 50 fighters in three days of clashes. Residents of the area say the casualties are higher.
At least four Afghan security officers have also been killed. Aerial bombardments continued on Wednesday.
Ismail, who lives in the Arghandab district, north of Kandahar, said: "The fighting is still going on with the Taliban. We’ve all left our places ... but maybe there are a few people left behind."
Towards Kandahar
Qari Mohammad Yousuf, a Taliban spokesman, said fighters had captured seven checkpoints around Arghandab.
Al Jazeera's Hamish MacDonald in Kabul says that the Taliban claims to control three-quarters of Arghandab, a district close to Kandahar.
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Al Jazeera aired exclusive video of the
ongoing battle in Kandahar province |
He said: "Control of this area would put the Taliban within striking distance of Kandahar, southern Afghanistan's largest city.
"The city, however, is a major base for the US military and at this stage it is clear the Taliban would struggle to drive out the international forces."
It is the first time since 2001 that Taliban fighters have been able to control the area.
On Tuesday, US-led multinational troops and Afghan forces killed several Taliban fighters, the US military said.
The fighters were killed in Ghazni province, southwest of the capital, Kabul, after they came under fire while conducting a search operation.