Spokesman Mohammad Naeem told Al-Jazeera Mubasher TV that no diplomatic body or any of its headquarters was targeted, saying the group assured everyone it would provide safety for citizens and diplomatic missions.
"We are ready to have a dialogue with all Afghan figures and will guarantee them the necessary protection," he told the Qatar-based channel on Sunday.
He said the group took every step responsibly and was keen on having peace with everyone.
Earlier, Taliban spokesman Suhail Shaheen told the Associated Press the militant group was holding talks aimed at forming an "open, inclusive Islamic government".
Taliban insurgents entered Kabul on Sunday and President Ashraf Ghani left Afghanistan saying he wanted to avoid bloodshed, bringing the Islamist militants close to taking over the country two decades after they were overthrown by a US-led invasion.
Naeem said of Ghani's escape it was not taken into account and "even those close to him did not expect it".
He said the group today was seeing the fruits of its efforts and sacrifices for 20 years: "We have reached what we were seeking, which is the freedom of our country and the independence of our people."
"We will not allow anyone to use our lands to target anyone, and we do not want to harm others," Naeem said the group would not interfere in the affairs of others and, in return, would not allow interference in its affairs.
"We do not think that foreign forces will repeat their failed experience in Afghanistan once again," Naeem said, adding the group was ready to deal with the concerns of the international community through dialogue.