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Pakistani officials continue to offer behind-the-scenes support for the covert program and provide intelligence for strikes despite publicly chastising the U.S. each time an attack occurs.

Mr. Levin expressed frustration with the criticism, noting that Pakistani Foreign Minister Shah Mehmood Qureshi had acknowledged a significant improvement in the accuracy of these strikes in a recent meeting.

“When a mistake is not made, when a target is hit accurately … I’ve got problems with the public attack which then creates that huge animosity against us when it is, number one, done with at least the acquiescence of the Pakistan government; and number two, when they are failing to go after those targets,” Mr. Levin said.

Mr. Ackerman said Pakistani cooperation with the U.S. should not be confused with affection.

Pakistan does work with us and — as it serves their interests — they will continue to work with us. But they’re never going to love us, and they’re never going to trust us. And we need to play by those same rules,” he added.

Mr. Wolf has, meanwhile, has recommended that an “Afghanistan-Pakistan Study Group” be set up to spell out U.S. goals in both countries.

“You are seeing the support for what the [Obama] administration is doing beginning to erode somewhat. I think this [study group] could restore confidence,” Mr. Wolf said.