WASHINGTON: Five years after they were seized by an extremist network in the mountains of Afghanistan, an American woman, her Canadian husband and their children, all three born in captivity, are free after a dramatic rescue orchestrated by the U.S. and Pakistani governments and have left Pakistan, officials said Thursday.

The U.S. said Pakistan accomplished the release of Caitlan Coleman of Stewartstown, Pennsylvania, and her husband, Canadian Joshua Boyle.

The operation, which came after years of U.S. pressure on Pakistan for assistance, unfolded quickly and ended with what some described as a dangerous raid, a shootout and a captor's final, terrifying threat to "kill the hostage." Boyle suffered only a shrapnel wound, his family said.

U.S. officials did not confirm the details.

A U.S. military official said that a military hostage team had flown to Pakistan Wednesday, prepared to fly the family out. The team did a preliminary health assessment and had a transport plane ready to go.

But sometime after daybreak Thursday, as the family members were walking to the plane, Boyle said he did not want to board.

Boyle's father said his son did not want to board the plane because it was headed to Bagram Air Base and the family wanted to return directly to North America. Another U.S. official said Boyle was nervous about being in "custody" given his family ties.

He was once married to Zaynab Khadr, the older sister of former Guantanamo Bay detainee Omar Khadr and the daughter of a senior al-Qaida financier. Her father, the late Ahmed Said Khadr, and the family stayed with Osama bin Laden briefly when Omar Khadr was a boy.

The Canadian-born Omar Khadr was 15 when he was captured by U.S. troops following a firefight and was taken to the U.S. detention center at Guantanamo Bay. Officials had discounted any link between that background and Boyle's capture, with one official describing it in 2014 as a "horrible coincidence."

The U.S. Justice Department said neither Boyle nor Coleman is wanted for any federal crime.

The couple told U.S. officials and their families they wanted to fly commercially to Canada.

Boyle's father called the rescue a "miracle." Coleman's parents, Jim and Lyn Coleman, meanwhile, posted a statement on the door of their Pennsylvania home expressing joy. Lyn Coleman said "I am in a state of euphoria, stunned and overjoyed," in an interview with ABC News.

The developments came rapidly Wednesday afternoon nearly five years to the day after Coleman and Boyle lost touch with their families while traveling in a mountainous region near the Afghan capital of Kabul.

Coleman's parents last had a conversation with their son-in-law on Oct. 8, 2012, via an email sent from an internet cafe he'd described as being in an "unsafe" part of Afghanistan. From then on, there were only desperate hostage videos released by their captors and hand-scrawled letters mailed home.

"I pray to hear from you again, to hear how everybody is doing," read one letter the parents shared with the online Circa News service in July 2016, in which Coleman revealed she'd given birth to a second child in captivity. It's unclear whether they knew she'd had a third.

Boyle's parents say their son told them in a letter that he and his wife pretended to the children that their signs of captivity were part of a game being played with guards.

Canadian Foreign Minister Chrystia Freeland said her country was "greatly relieved" the family was safe, and she thanked the U.S., Afghan and Pakistani governments for their efforts.

U.S. officials have said that several other Americans are being held by militant groups in Afghanistan or Pakistan.

They include Kevin King, 60, a teacher at the American University of Afghanistan in Kabul who was abducted in August 2016, and Paul Overby, an author in his 70s who had traveled to the region several times but disappeared in eastern Afghanistan in mid-2014.