Afghan civilians are being stripped of their weapons because they can now "feel safe" and no longer need them, the Tablian has claimed.
"We understand people kept weapons for personal safety," the spokesperson said. "We are not here to harm innocent civilians".
The comments came as footage from Kabul airport showed chaos break out as people tried to board planes in a bid to escape the Islamist group, with some clinging onto to a US military aircraft.
At least seven people are reported dead and video shared on social media appears to show people falling from the US C-17 plane as it takes off.
Taliban fighters faced next to no resistance as they entered Kabul, seizing power some 20 years after they were ousted by British and American troops.
One man said members of the group arrived at his business on Monday to ask about weapons stored there by a security team.
Saad Mohseni, a Kabul resident and director of the MOBY media company, wrote on Twitter: "Taliban soldiers inside our compound in Kabul.
“So far they are polite, enquiring about our weapons (of the security team)."
He added: "They are collecting govt issued weapons. They have also agreed to keep the compound safe".
The militants have vowed not to harm civilians or carry out reprisal attacks against former government officials, insisting the transfer of power will be peaceful.
However, there have already been a number of reports of executions of people who have been branded "traitors".
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