"The stupidity and evil of the Haqqani network's kidnapping of a pilgrim and his heavily pregnant wife engaged in helping ordinary villagers in Taliban-controlled regions of Afghanistan was eclipsed only by the stupidity and evil of authorising the murder of my infant daughter", Mr Boyle said.
Mr Boyle said his wife was raped by a guard who was assisted by his superiors.
Pakistan's foreign ministry spokesman, Nafees Zakaria, said the Pakistani raid that led to the family's rescue was based on a tip from United States intelligence and shows that Pakistan will act against a "common enemy" when Washington shares information. The birth of the fourth child had not been publicly known before Boyle appeared before journalists at the Toronto airport.
The Taliban in a statement on Sunday denied Boyle's claims.
He said the Haqqani leadership authorized the murder of his infant daughter in retaliation for his refusal to accept an offer from the kidnappers, but did not elaborate on the offer. The statement further disputed Boyle's allegation that his wife was raped, saying that the family members had not been separated for even a minute after their capture.
"Today, we join the Boyle family in rejoicing over the long-awaited return to Canada of their loved ones", the Canadian government said in a statement.
An Afghanistan man emailed two videos of Coleman and Boyle pleading for help to their families in 2013, which was later released by Coleman's family in June 2014.
"We took care of this family like our own family members and special guests, but after frequent flying of USA drones on Kurram tribal region and its adjoining areas, it was chose to move them to a safer place", a Taliban official told Reuters.
The couple were abducted in October 2012 while in Afghanistan as part of a brief backpacking trip and held by the Haqqani network, which has ties to the Taliban and is considered a terrorist organization by the USA government. It was a risky venture for any couple traveling without escort, especially since Coleman was pregnant with their first child.
The maiden quadrilateral meet comes in the wake of the US President Donald Trump announcing his Afghan policy and mounting massive pressure on Pakistan to launch a crackdown against Taliban and terrorism infrastructure.
The rescue operation appeared to have unfolded quickly and ended with what some described as a risky raid, a shootout and a captor's final, terrifying threat to "kill the hostage". He pleaded guilty to murder for killing a US soldier but later recanted, claiming he'd been abused while incarcerated and coerced into making the plea.
A Pakistani channel broadcasts a report about western couple, seen at a local electronic shop in Islamabad, Pakistan, Thursday, Oct. 12, 2017. Another U.S. official told the AP that Boyle was nervous about being in "custody" given his family ties. It's unclear whether they knew she'd had a third.
The U.S. military referred all questions to the State Department.
"To pursue personal pleasure or comfort while there is still deliberate and organised injustice in the world would be a betrayal of all I believe, and tantamount to sacrilege", he wrote.
The AP reported in June 2014 about the existence of videos received by Coleman's father in which the couple - Coleman, in a conservative black garment and Boyle with a long, untrimmed beard - implored the USA government to help free them.
The youngest child is understood to be in poor health.
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