According to the broadcaster, Abdullah dismissed these statements, adding that the Afghan people were on the front line of the fight against Daesh.
Abdullah noted that the country's security forces were monitoring Daesh activity in the northern regions and receiving support from NATO forces.
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Commenting on the upcoming Moscow format meeting on Afghan settlement, scheduled for September 4, Abdullah said that Kabul welcomed any "honest efforts" by any country to bring peace and stability to the country.
Afghanistan has long been suffering from unstable political, social and security situation due to the simmering Taliban insurgency. The violence is exacerbated by the activities of various terrorist groups, including Daesh.
Last week, the Afghan government said that it would participate in the Moscow-format consultations on Afghanistan only if the Taliban agreed to direct talks with representatives of the Afghan government on the sidelines of this event.
*Daesh (also known as ISIS/ISIL/IS) and the Taliban are terrorist groups, banned in Russia