"The presence of terrorist sanctuaries and support networks in Pakistan continue to cause trouble inside Afghanistan," Abdullah said during his address to the United Nations General Assembly yesterday on the opening day of its 70th annual General Debate.
"The Haqqani network has been identified as a main culprit and needs to be dismantled as has been our demand in the past," he said.
Abdullah said some of the attackers in Kunduz had come from abroad, and said, "We call on Pakistan to do what its leadership promised to us a few months ago when they agreed to crack down on known terror outfits."
"We also call on regional stakeholders and our international partners to realise the gravity of the situation, and use their good offices or any effective means to support our aspirations for a genuine and durable confidence-building process leading to talks with willing Taliban and other armed opposition groups," he said.
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He also noted that the world faces a host of mainly human-made threats and called for United Nations reforms to deal speedily and effectively with the challenges ahead.
Kunduz is the first provincial capital seized by the Taliban since they lost power in the US-led invasion in 2001.
The attack on the northern city came as President Ashraf Ghani completed a year in office.
The attack on Kunduz began at dawn yesterday as fighters fell upon the city from different directions. They captured key buildings and freed about 500 prisoners, including members of the Taliban, from the jail.