The militant group has made rapid advances across southern Afghanistan overnight as US and other foreign forces near a complete withdrawal.
The speed of the Taliban offensive raises questions of how long the Afghan government forces can stop the militants from reaching Kabul.
Fighting in Afghanistan's long-running conflict has escalated dramatically since May, when the US-led military coalition began the final stage of a withdrawal set to be completed before the end of the month.
The failure of US-led forces to address grassroots issues and the absence of a strong Afghan government has led to the resurgence of the Taliban, experts say.
Heavy fighting continues in at least three provincial capitals, with government forces beating back fresh attacks to keep Helmand’s Lashkar Gah from falling to the insurgent group.
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.
The Kandahar province of Afghanistan has been the theatre of fierce fighting since the insurgents took control of the key Spin Boldak border crossing with Pakistan earlier this month.
Pakistan's military said it had granted asylum to at least 46 Afghan soldiers who crossed the Durand Line into northwestern Pakistan after their military posts in Afghanistan were overrun by Taliban insurgents.
Local officials say 22,000 families have been displaced in the past one month in Kandahar, as fighting between Taliban and government forces continues outskirts of the city after NATO troops withdrawal from the country.
About 50 Indian personnel, including some six diplomats, pulled from consulate, security sources say, as Taliban fighters clash with government troops in their former bastion in southern Afghanistan.
Taliban fighters do not have any organised capacity but have demonstrated they can fire modified rockets from vehicles and create panic, a security official says.
Hundreds of Afghan soldiers cross over to Tajikistan as Taliban fighters capture more territory across Afghanistan's rural areas, including a key Kandahar district, in fresh fighting.
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