The statement came at the end of the first direct talks between the former foes since the withdrawal of U.S. troops at the end of August.
There was no immediate comment from the U.S. on the weekend meeting.
The Taliban commented that talks held in Doha, Qatar, 'went well,' with Washington freeing up humanitarian aid to Afghanistan after agreeing not to link such assistance to formal recognition of the Taliban.
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The United States pledged that the talks were in no way a preamble to recognition of the Taliban, who swept into power August 15 after the U.S.-allied government collapsed.
The Taliban's rapid takeover of the country has scrambled the nation's already-weak economy.
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Banks were closed for about two weeks in the country, forcing unemployed Afghans to sell their household goods just to survive.
Taliban political spokesman Suhail Shaheen also told The Associated Press that the movement's interim foreign minister assured the U.S. that the Taliban are committed to seeing that Afghan soil is not used by extremists to launch attacks against other countries.
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On Saturday, however, the Taliban ruled out cooperation with Washington on containing the increasingly active Islamic State (IS) group in Afghanistan.
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IS, a sworn enemy of the Taliban, has claimed responsibility for a number of recent attacks, including Friday's suicide bombing that killed 46 minority Shiite Muslims. Washington considers IS its greatest terrorist threat emanating from Afghanistan.
'We are able to tackle Daesh independently,' Shaheen insisted when asked whether the Taliban would work with the U.S. to contain the Islamic State affiliate.
Bill Roggio, a senior fellow at the Foundation for Defense of Democracies who tracks militant groups, agreed the Taliban do not need Washington's help to hunt down and destroy Afghanistan's IS affiliate, known as the Islamic State in Khorasan Province, ISKP.
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The Taliban 'fought 20 years to eject the U.S., and the last thing it needs is the return of the U.S. It also doesn't need U.S. help,' stated Roggio, who also produces the foundation's Long War Journal. 'The Taliban has to conduct the difficult and time-consuming task of rooting out ISKP cells and its limited infrastructure. It has all the knowledge and tools it needs to do it.'
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The IS affiliate doesn't have the advantage of safe havens in Pakistan and Iran that the Taliban had in its fight against the United States, Roggio said. However, he warned that the Taliban's longtime support for al-Qaida makes them unreliable as counterterrorism partners with the United States.
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The Taliban gave refuge to al-Qaeda before it carried out the 9/11 attacks. That prompted the 2001 U.S. invasion of Afghanistan that drove the Taliban from power.
'It is insane for the U.S. to think the Taliban can be a reliable counterterrorism partner, given the Taliban´s enduring support for al-Qaida,' Roggio conceded.
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