Reading from a statement after the family arrived in Toronto on Friday, Boyle, a Canadian citizen, made his allegations calmly and declined to elaborate.
"The stupidity and the evil of the Haqqani network in the kidnapping of a pilgrim . . . was eclipsed only by the stupidity and evil of authorizing the murder of my infant daughter," Boyle said, adding that the killing was in "retaliation for my repeated refusal to accept an offer" that the Haqqanis had made. He did not specify what the offer was.
He also denounced "the stupidity and evil of the subsequent rape of my wife, not as a lone action by one guard, but assisted by the captain of the guard and supervised by the commandant."
Pakistani officials would not comment on the allegations, and the State Department declined to comment, citing respect for the family's privacy. A Taliban spokesman said the rape and murder claims "have no basis at all," adding that the baby died in a miscarriage.
The Haqqani network, a family-based guerrilla group with roots in southeastern Afghanistan, is closely affiliated with the Taliban and is considered the most lethal and resilient enemy of U.S. forces there. It is headquartered in the area of the Pakistan border and also held U.S. Army Sgt. Bowe Bergdahl for five years, during which he reportedly was kept chained or in a cage and was frequently beaten. Bergdahl was released in a 2014 in exchange for five Taliban figures held by the United States.
"Generally, they don't treat prisoners humanely," said Hamed Daqeeq, a former Afghan government official who is now a political analyst in Kabul. In the past, freed detainees "spoke of being tortured and beaten badly by the group," he said.
The Haqqanis, many of whose leaders have been killed in U.S. drone strikes in Pakistan over the years, also are allegedly responsible for the 2009 suicide attack on a CIA facility near the eastern Afghan city of Khost, in which seven CIA officers and contractors were killed.
Coleman and Boyle were abducted in October 2012 while traveling in a remote area of Afghanistan outside Kabul.
Boyle was previously married to the sister of Omar Khadr, once the youngest detainee at the U.S. military detention center at Guantanamo Bay after he pleaded guilty to killing a U.S. Special Forces medic.
Boyle said he and Coleman were in Afghanistan to help villagers "who live deep inside Taliban-controlled Afghanistan where no NGO [nongovernmental organization], no aid worker and no government has ever successfully been able to bring the necessary help." The couple had previously said that they were on a six-month hiking trip through Central Asia.
At the time, Coleman was pregnant, and she gave birth to her children in captivity. Before the new allegations, the couple was believed to have three children, who were rescued with their parents.
In a video released last year, Coleman said her family was in a "Kafkaesque nightmare" and that her children had "seen their mother defiled."
U.S. officials in recent months had suspected that Boyle, Coleman and their children were being held inside Afghanistan, although there was never enough information to locate them in "real time," said a former U.S. official who spoke on the condition of anonymity to discuss sensitive intelligence.
The couple and their children were being spirited across the border into Pakistan when U.S. officials appear to have learned of their whereabouts and passed the intelligence to Pakistani officials, who carried out the rescue.
According to Pakistani military officials and Boyle's account, the operation appeared to have 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 told his parents that he, his wife and their children were intercepted by Pakistani forces while being transported in the back or trunk of their captors' car and that some of his captors were killed. He suffered only a shrapnel wound, his family said.
U.S. officials did not confirm those details.
But officials in Islamabad were eager to share the drama behind an operation that may help pull their country back into favor with the United States after President Trump chastised Pakistan as offering "safe havens" to terrorists and hinted at possible sanctions. Pakistan denies providing havens for militants.
On Saturday, Maj. Gen. Asif Ghafoor, spokesman for the Pakistani army, said the rescue effort began after a U.S. diplomat informed Pakistani officials that the family was being moved.
The rescuers fired at the vehicles' tires and cordoned the one that was carrying the family, he said.
"Our first priority was that the captives are brought out safely. We wanted to isolate the terrorists and captives, and we wanted to come between the terrorists and hostages, which we did, so that the captives remain safe," Ghafoor said.
He did not address Boyle's allegations of rape and murder.
A U.S. military official said that a military hostage team had flown to Pakistan on Wednesday prepared to fly the family out. The team conducted a preliminary health assessment and had a transport plane ready, but sometime after daybreak Thursday, as the family members were walking to the plane, Boyle said he did not want to board, the official said. In his statement Friday in Toronto, Boyle denied reports that he refused to board the plane.
The family was flown instead to Toronto, where, according to reports, Boyle said that one child was malnourished and had to be force-fed by their Pakistani rescuers.
He called on the Taliban to bring the Haqqani network to justice.
In a video recorded in Pakistan after the rescue and released Saturday by the Pakistani military, Boyle praised the country's military for its bravery and professionalism, saying that a car of one rescue team was "riddled with bullets" and that the Pakistani agents "got between the criminals and the car to make sure that . . . my family was safe."
The Western world "will look at Pakistan a little bit differently now after this has happened," Boyle said, "and will understand that it is not a third-world disaster area run by incompetent people at all. It is actually on the world stage and on the front lines."