Afghanistan's president said Thursday 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 strength, referring to Pakistani President Gen. Pervez Musharraf.

Karzai equated cooperating with terrorists to "trying to train a snake against somebody else."

"You cannot train a snake. It will come and bite you," he said.

Karzai and Musharraf have spent much of this week's U.N. General Assembly meeting trading barbs and criticizing the other's efforts to fight terrorists along their long, remote, mountainous border. President George W. Bush will likely try to diffuse those tensions at a joint meeting with the leaders next week.

CountryWatch: Afghanistan

Karzai, speaking at the Council on Foreign Relations, played down a growing Taliban-led insurgency in Afghanistan that aims to topple his U.S.-backed government.

"They are there in the form of killers of teachers, killers of clergymen, killers of school children, destroyers of schools, destroyers of clinics, destroyers of reconstruction activity and harassment to the population.

"Is that strength? No. Is it popular base? No," he said.

Karzai said his government has not stopped the Taliban from committing acts of terrorism "because of lack of proper police force, because of lack of proper military force and because of the general inability of the country, having been weakened by years of war and destruction, to provide that kind of protection to the population."

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."

Pakistan rejects the accusation that it is not doing enough, pointing out that it has deployed 80,000 troops along the porous border. Musharraf said Wednesday that "the problem lies in Afghanistan, and that is creating the problem in Pakistan."

The leaders' comments come weeks after Pakistan signed a truce with militants in a tribal province where the government has little control.

The deal requires Pakistani troops to end military action against the fighters in return for the militants stopping attacks on Pakistani forces and not crossing into Afghanistan to launch ambushes.

Another spat between the neighbors focuses on the whereabouts of Taliban chief Mullah Omar and Al Qaeda leader Usama bin Laden.

Karzai said Omar is "for sure" in Pakistan. Musharraf "knows it and I know it," Karzai said. "He's truly there."

On Wednesday, Musharraf insisted that the Taliban leader is in Afghanistan, "very much in his own area, with his own people." Afghanistan, Musharraf said, needs "to go for him. Military action is required against him."

On bin Laden, Karzai said: "If I told you he was in Pakistan, President Musharraf, my friend, would be mad at me. But if I said he was in Afghanistan, that would not be true."