Afghanistan's president has said that the Taliban was not gaining strength in his country and suggested that Pakistan's toleration of militants had helped make Afghanistan unstable.
President Hamid Karzai said some in the region used extremists to maintain political power, referring to Pakistani President Gen Pervez Musharraf.
Karzai equated cooperating with terrorists to "trying to train a snake against somebody else." He said: "You cannot train a snake. It will come and bite you".
Separately, Musharraf responded to comments from US President George W Bush, who told CNN he would act to kill or capture Osama bin Laden if he had intelligence that the al-Qaida leader was in Pakistan.
"No. We wouldn't like to allow that at all," Musharraf told reporters Wednesday at the United Nations. "We would like to do it ourselves."
Karzai and Musharraf have spent much of this week's UN General Assembly meeting trading barbs and criticising each other's efforts to fight terrorists along their long, remote, mountainous border.
Bush will likely try to diffuse those tensions at a joint meeting with the leaders next week.
Karzai, speaking at the Council on Foreign Relations, played down a growing Taliban-led insurgency in Afghanistan that aims to topple his US-backed government.
He said the Taliban had killed teachers and children and destroyed clinics and schools. "Is that strength? No. Is it popular base? No."
Referring again to Musharraf, Karzai said: "Some of these regimes are definitely using extremism as an instrument of policy, and that is why Afghanistan has suffered.