Afghanistan has now been "emancipated" and the Taliban seeks no revenge after regaining control of the country, the group has said in a news conference.
A spokesman said "we want the world to trust us" and appealed to people not to interfere in the transfer of power.
He said the group's top priority was to create "law and order" for the capital Kabul, and assured the people of the city they would "live in peace".
Speaking to reporters, the spokesman said the Taliban "don't want any internal or external enemies" and also said "we will work with" the world to create a successful Afghanistan.
The news conference, the first staged by the militant group after it seized control of Afghanistan in a rapid wave over the weekend, began with a recitation from the Quran by Taliban spokesperson Zabihullah Mujahid.
It comes after the militant group told Sky News that women would be able to be educated up to university level and will have the right to work in Afghanistan.
The spokesman said that women would be allowed to work in schools and hospitals.