Tuesday’s statement came days after ISIS claimed responsibility for a bomb attack in the eastern city of Jalalabad.
Since toppling the Western-backed government in Kabul last month, the Taliban has faced pressure from the international community to break with al-Qaeda, the group behind the September 11, 2001 attacks on the United States.
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At the same time, they have had to face a series of attacks claimed by the ISIS affiliate, with which they have been in conflict for several years over a mix of economic and ideological strife.
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Taliban spokesman Zabihullah Mujahid rejected accusations that al-Qaeda maintains a presence in Afghanistan. He has repeatedly promised no attacks on a third country from Afghanistan by the al-Qaeda militant movement.
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“We don’t see anyone in Afghanistan who has anything to do with al-Qaeda,” he told a news conference in Kabul.