(CNN) -- NATO said Monday that it has found no evidence backing up an Afghan government claim that armed people who may be U.S. special forces carried out acts of torture and murder.

"We will not start with the assumption that the allegations are true," NATO's International Security Assistance Force said in a Twitter post. "We looked into the allegations" and "found no supporting evidence for them."

The NATO response comes a day after Afghanistan's government demanded that U.S. special forces leave Wardak province, a key area west of the Afghan capital where the alleged horrors took place. The Afghanistan National Security Council also said the ISAF must stop all special force operations in the province.

Force officials are planning talks with Afghan officials over the allegations of wrongdoing, the ISAF said. The U.S. military has said it is investigating.

"Until we have a chance to speak with Afghan officials, we can't comment further on the statements of yesterday," the ISAF said Monday.

At a meeting of the Afghan council, led by President Hamid Karzai, "it became clear that armed individuals named as U.S. special force stationed in Wardak province engage in harassing, annoying, torturing and even murdering innocent people," Karzai's office said in a statement Sunday. The statement did not indicate who "named" the group a U.S. special force.

It added that the United States rejects any suggestion that its special forces carried out any such operation.

Nine people "disappeared in an operation by this suspicious force," the president's office said. And in another incident, a student was taken from his home at night, and his "tortured body with throat cut was found two days later under a bridge."

"Such actions have caused local public resentment and hatred," Karzai's office said.

Last April, the United States and Afghanistan signed a deal giving Afghan authorities an effective veto over controversial special forces missions.

The agreement prevents the ISAF from conducting such operations without the explicit permission of Afghan officials, a senior NATO official said. And special operations forces will operate under Afghan law, said a statement from Karzai's office.

The complex system fully "Afghanized" such operations, putting Afghan commandos in the lead and giving American special forces a "training and support role," a senior Afghan official said.

Under the deal, U.S. special forces would be on the ground but would not enter an Afghan's home unless specifically asked to do so by the Afghan commandos leading the operation, or by other Afghan officials, a senior NATO official said.

This pact followed months of recriminations against special operations raids, particularly at night, that have deeply offended some Afghans angry about foreigners entering their homes.

U.S. officials have said such raids are vital to NATO's operation against insurgents.

CNN's Greg Botelho, Barbara Starr and Nick Paton Walsh contributed to this report.

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