The Taliban are reported to have raised their flag above a key border post between Afghanistan and Pakistan, and claim it is now under their control.
Videos being shared on social media show the white flag fluttering above the Spin Boldak crossing near Kandahar.
Afghan officials have denied the post has fallen, although pictures on social media show the militants chatting to Pakistani border guards.
The BBC has been told the Taliban took the border crossing with no resistance.
In recent weeks, the militants have made rapid advances across the country, seizing a series of border posts from Afghan forces, including crossings with Iran, Tajikistan and Turkmenistan.
It comes as the US withdraws its forces from Afghanistan ahead of an 11 September deadline set by President Joe Biden.
The Taliban - a fundamentalist Islamist militia who were pushed out of power by the US invasion nearly 20 years ago - have also seized control of a number of key roads as they seek to cut off supply routes to major cities.
The border post, which divides the Afghan town of Spin Boldak in Kandahar province on one side and the Pakistani town of Chaman on the other, is the second busiest crossing between the countries. It links the city of Kandahar to Pakistan's ports, and sees some 900 trucks pass through each day.
The crossing would be a major prize - symbolically and strategically - if the Taliban continue to hold it, according to BBC correspondent Lyse Doucet.
It would give them significant customs revenue from the trade which flows back and forth and would provide direct access to areas in Pakistan, where Taliban leaders and fighters are known to have been based for many years, she says.
The BBC has not been able to independently verify the reports but Pakistani officials confirmed the Taliban had taken the post. Journalists and the public have been told not to approach the border from the Pakistan side, and there is an urgent security meeting under way there, our reporter in Quetta has been told.
Locals have also said the Taliban - which promised residents and traders that their "security is guaranteed" in a statement earlier on Wednesday - are in the Afghan town.
One shop owner told AFP the militants could be seen in the "bazaar, in police HQ and custom areas," while fighting could be heard nearby.
But Afghan interior ministry spokesman Tareq Arian earlier insisted to AFP that while there had been "some movements near the border... security forces have repelled the attack".
Afghan President Ashraf Ghani had promised civilians on Tuesday that "the Taliban's backbone will be broken", and the lost territory would be won back.
But his forces have been struggling to halt the Taliban's advance through the country, which has sped up since a 2020 deal struck with former US President Donald Trump's administration.
Under the terms of that deal, the US and its Nato allies agreed to withdraw all troops in return for a commitment by the militants not to allow any extremist group to operate in the areas they control.
But the Taliban did not agree to stop fighting Afghan forces. The militants are now in talks with the Afghan government - something they previously refused to do - but show no sign of stopping their attacks, with talks barely progressing.