"There are very high-level Taliban leaders who have sought to reach out to the highest levels of the Afghan government, and they have done that," Petraeus told reporters after a tour of a detention facility for suspected insurgents at Bagram, the largest US base in Afghanistan.
Afghan government officials, however, said the Taliban officials aren't senior leaders.
Why Pakistan condemned these attacks
The Pakistani protest appeared to be intended mostly for a domestic audience that deeply opposes US attacks on insurgent strongholds on the Pakistani side of the border as violations of its country's sovereignty.
The ISAF airstrikes Saturday were "a clear violation and breach of the UN mandate under which ISAF operates," Pakistani Foreign Ministry spokesman Abdul Basit said in a statement. "In the absence of immediate corrective measures, Pakistan will be constrained to consider response options."
Pakistan lodged an official protest with ISAF, he said.
Basit didn't elaborate on what "corrective" steps Pakistan was seeking or what responses it would consider if those steps weren't taken.
The first cross-border air strike occurred after "a significant number" of insurgents launched an attack from Pakistani territory on a remote Afghan National Army base just inside Afghanistan's eastern Khost province, ISAF said in its statement.