WASHINGTON — A C.I.A. drone was circling a remote valley in northwest Pakistan last month when it picked up an unusual sight: a young woman and children in a militant camp. To intelligence analysts, she appeared to be an American abducted five years earlier while backpacking in Afghanistan with her Canadian husband.

The grainy images were a breakthrough. Military planners mobilized members of the Navy’s SEAL Team 6, an elite group of commandos, to mount a rescue, according to senior American officials. But the operation was called off amid concerns, and days later, the C.I.A. watched in alarm as militants drove the family out of the camp and across Pakistan’s lawless tribal lands.

The top American diplomat in Pakistan, Ambassador David Hale, turned to his host country, one of the officials said, delivering an urgent message to the Pakistani government: Resolve this, or the United States will.

The implication was clear. If the Pakistanis did not act decisively, the United States would set aside its unease and launch a raid deep inside the country to free the family. It would be another humiliating episode for the Pakistani government, reminiscent of the operation that killed Osama bin Laden in 2011, conducted by the same elite Navy SEAL commandos well into Pakistan without its government’s knowledge. And a failure to act would underscore American officials’ belief that the Pakistani government gives safe haven to the Taliban-linked Haqqani network that had kidnapped the family.