The top U.S. military officer said on Friday that he thinks it is possible that the Pakistani military can shutdown Taliban hideouts on its soil to prevent insurgents from moving back and forth across the long, porous Afghan-Pakistan border.

A day after President Barack Obama released a review of the U.S. war strategy, Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, told reporters in Kabul that fixing the problem is critical to making progress in the war. But he said he’s encouraged by what Pakistan has already done to go after insurgents on its side of the border.

“I certainly think it is very possible that the Pakistani military will achieve the goal,” he said.

A five-page public summary of the classified White House Afghan war review said dealing with safe havens would require greater cooperation with Pakistan along the border. The areas of most concern — the Pakistani provinces of North Waziristan and Baluchistan — are not mentioned by name.

Pakistan has made progress against safe havens over the past year in operations that have taken a toll on its forces, the summary said. But Pakistani authorities have almost exclusively focused on militants who pose a threat inside Pakistan. So far they have refused a U.S. request to take on militants in North Waziristan, the place used most frequently to target U.S. forces.

Earlier, Gen. David Petraeus, the top commander of U.S. and NATO forces in Afghanistan, also highlighted Pakistan’s efforts to rout militants and a new willingness to cooperate with U.S. forces on operations that span the eastern border. He gave two recent examples where U.S. and Pakistani forces made a squeeze play around militants.

“The Pakistani leadership is clear about the goal,” Gen. Petraeus said. “I think there is general recognition that ... extremists of any type on Pakistani soil are a source of problems.”

The Taliban on Friday rejected the review of Mr. Obama’s year-old war strategy in Afghanistan, saying that it has failed on both the military and the civil administration fronts.

In an e-mailed statement, Taliban spokesman Zabiullah Mujahid said the last nine years of war had proven that increased troop levels had no effect.

“It is a failed strategy, not only on the military side but also in civilian and administrative affairs. Public services in Afghanistan have failed. Corruption, insecurity and also the civilian casualties are a result of failed American strategy,” Mujahid said.

Adm. Mullen spoke to reporters in the Afghan capital alongside Karl Eikenberry, the U.S. ambassador to Afghanistan, who said the existence of insurgent sanctuaries in Pakistan “makes delivery of peace and stability here in Afghanistan very difficult.”

Adm. Mullen accentuated progress being made in the war, saying that insurgents were being pushed out of Afghan cities and towns.

He said progress on the battlefield needs to be matched by gains in governance.

“Many of our accomplishments, even the ones I saw down south, are tenuous and can be lost,” Adm. Mullen said. “Indeed, they will be lost if good governance and responsible civic responsibilities are not assumed by the Afghan government with the same alacrity and the same courage as that shown by troops on the ground. We can take nothing for granted at this point.”

This year has been the deadliest in the war for U.S. forces. At least 480 American troops have been killed, compared to 317 last year and 155 in 2008.

NATO said two service members with the international force were killed on Friday — one following a bomb attack in southern Afghanistan and the other in an insurgent attack in the east of the country. It did not provide the nationalities of either or give the locations of the attacks.

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