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.
Zabihullah Mujahid said the group’s top priority is to create “law and order” for the capital Kabul – and assured the people of the city they would “live in peace”.
Afghanistan live updates: All the latest as the Taliban establish new government
Speaking to reporters, Mr Mujahid also assured of the safety of those who had worked with American and allied forces.
He said the Taliban does “not want them to leave the country” but wants them to use their skills to serve the new regime – and they “will be pardoned”.
The Taliban “don’t want any internal or external enemies”, he said, 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 spokesman Mr Mujahid.
It comes after the militant group told Sky News that women would be able to pursue education up to a university level and will have the right to work in Afghanistan.
Taliban spokesperson Zabiullah Mujahed says the group 'recognises the rights to women that Islam gave them', adding women can 'work, go to school, and can work in schools and in hospitals'.
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However, the Taliban said: “Our women are Muslim and will be happy to live within the framework of our law.”
Mr Mujahid said that women would be allowed to work in schools and hospitals.
He said Afghans gave “great sacrifices for the establishment of an Islamic government and they have the right to implement Shariah law”.
Different countries “have their own laws” and “Afghans have the rights to live under their own laws”, he added.
He said he can also “assure the world”, including the USA, that Afghanistan soil will not be used against any country in the world.
The group said it is “still working” on the set-up of the government, but once the war is over, its focus will be on building up the economy.
The new government is also committed to a “free and independent media”, Mr Mujahid claimed, however, he said he had “requests”, including that “Islamic values should be taken into account when it comes to the activities of the media”.
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He said the media “should not work against national values, against national unity”.
Taliban fighters have been directed not to harm anybody and “not to knock at any door unnecessarily”. He says they have also been told not to stop any car unnecessarily.
Analysis by Deborah Haynes, foreign affairs editor
They have swept into power but there isn’t yet a government being formed. They said at the end that they’re speaking to all the different parties and that they want everybody to be involved. At the same time they said that it will be a strong Islamic government.
The other top lines are that there would be an amnesty for people who’d worked with the previous government or other countries, that they didn’t have to leave the country. They appealed for Afghanistan’s bright young people to stay and work.
There will be a lot of doubt about whether that will play out in reality as there are already reports of armed men knocking on doors asking uncomfortable questions.
I thought it was striking that they kept saying women and girls would be allowed education up to university, they’ll be allowed to go to work, all in line with Islamic law.
But a female journalist asked if people like her, female journalists, would be allowed to work in the same way as the last 20 years. There wasn’t a straight answer to that question.
The one other key message, and they reiterated this twice, was that Afghanistan will not pose a threat to the rest of the world.
They were asked about the relationship with al Qaeda, a relationship that runs deep and that analysts don’t believe will be severed, but clearly the Taliban realised that if the country is used by terrorists it will draw international intervention once more.