The whereabouts of the hostages were located by a CIA drone in a remote valley in northwest Pakistan last month. The grainy images - captured by the drone - of a young woman and children in a militant camp were a "breakthrough", The New York Times reported, citing senior American officials.
Coleman, 31, was pregnant at the time of abduction. All the three children were born in captivity.
"Military planners mobilised members of the Navy's SEAL Team 6, an elite group of commandos, to mount a rescue," the paper said, quoting the officials.
The commandos of SEAL Team 6, tapped to rescue the family, started rehearsing. The raid was to take place not far from where the CIA had originally spotted the family, according to one military official.
Others voiced worries about the difficult terrain and the moon it was too bright for a nighttime airborne raid.
Days later, the CIA watched in alarm as militants drove the family out of the camp and across Pakistans lawless tribal lands.
On October 11, as they headed toward Kohat, a city farther inside Pakistan, American intelligence officials realised they could not let the opportunity to save the family slip by the United States had to act.
US Ambassador to Pakistan David Hale delivered an urgent message to the Pakistani government - "Resolve this, or the US will", the paper quoted one of the officials as saying.
"The implication was clear. If the Pakistanis did not act decisively, the US would set aside its unease and launch a raid deep inside the country to free the family," it said.
"The push worked. American officials said the Pakistanis acted quickly, intercepting the vehicle with Coleman and her family," the paper said.
Pakistani officials later said they acted within hours.
In a statement, the Pakistan Army said they recovered 5 Western hostages including 1 Canadian, his US National wife and their three children from terrorist custody through an operation based on actionable intelligence from US authorities.
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