Districts of Khinj and Unabah have been taken from so-called National Resistance Front, a Taliban spokesperson says, giving Afghanistan's new rulers control of four of province's seven districts.
Flights from Kandahar airport were cancelled when rockets hit the runway, an official said, as the Taliban pressed on with their sweeping offensive across the country.
"Although we (Taliban) have the upper hand on the battlefield, we are very serious about talks and dialogue," a spokesperson of the Afghan insurgent group tells Reuters.
As a Taliban offensive spreads across Afghanistan, Ashraf Ghani will be hoping for a significant commitment of aid post troop withdrawal with Joe Biden expected to pressure the Afghan leader to strike a deal with the insurgents.
Key politicians with background of anti-Taliban or anti-Soviet resistance are converging in their areas of influence to mobilise forces for a likely face-off with the marching Taliban. But rights groups fear such militias could become abusive force.
US President Joe Biden has set May 1 as the official start of the withdrawal of the remaining forces from the war-torn country.
In a series of multiple, separate attacks on Afghan security forces in the country's north, a total of 37 Afghan security forces were killed in gun battles.
Abdul Aziz Beg, head of the provincial council in Badghis province, says the Taliban struck Afghan army positions from different directions. There are conflicting reports over the Taliban's claim.
Heavy fighting has broken out in the western Afghan city of Farah after the Taliban launched a major offensive overnight to capture the provincial capital.
US-led NATO soldiers are training the Afghan police, the army and other agencies as they wind down their commitments in the country.
Afghan security forces have driven Taliban back from Kunduz, after heavy fighting overnight in which dozens were killed and wounded
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