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Ban, in particular, pointed to a bomb attack on June 17 on a bus in Kabul that killed 35 people, mostly Afghan police trainers.
The attack has been claimed by the Taliban.
The statement from the UN chief also noted, "with deep sadness," that seven Afghan children were reported killed as a result of a recent coalition air strike in Paktika Province.
Meanwhile, Japan is today hosting an international conference aimed at strengthening efforts to persuade illegal armed groups in Afghanistan to put down their weapons.
Japanese Foreign Minister Taro Aso, in an opening speech, said the threat posed by such groups must be addressed urgently.
He said the "unfortunate truth" is that the "weak governance of the Afghan government" continues to hinder the country's reconstruction.
The conference is being attended by Afghan Vice President Abdul Karim Khalili and officials from 18 countries and international organizations.
Copyright (c) 2006. RFE/RL, Inc. Reprinted with the permission of Radio Free Europe/Radio Liberty, 1201 Connecticut Ave., N.W. Washington DC 20036. www.rferl.org