Freed Canadian hostage Joshua Boyle says the Haqqani terrorist group in Afghanistan killed his infant daughter in captivity and raped his wife during the years they were held hostage.

Key points: The couple was kidnaped while backpacking in 2012

The couple was kidnaped while backpacking in 2012 Ms Coleman was pregnant at the time and had three children in captivity

Ms Coleman was pregnant at the time and had three children in captivity Mr Boyle says the Haqqani group killed another child and raped Ms Coleman

He shared the details of his capture shortly after touching down in Toronto with his wife Caitlan Coleman and their three young children, five years after they were kidnapped.

Ms Coleman and Mr Boyle were rescued on Wednesday (local time), five years after they had been abducted by a Taliban-linked extremist network while in Afghanistan as part of a backpacking trip.

Ms Coleman was pregnant at the time, and gave birth four times while in captivity. Mr Boyle said one of the children was killed.

"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.

The birth of the fourth child had not been publicly known before the family arrived in Canada.

He added that one of his children was in poor health and had to be force-fed by their Pakistani rescuers.

He said they were rescued after "a gun battle in Pakistan."

Earlier, Mr 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.

US officials did not confirm those details.

"God has given me and my family unparalleled resilience and determination," Mr Boyle said in a written statement earlier.

Ms Coleman, wearing a tan-coloured headscarf, sat in the aisle of the business class cabin during the flight.

US State Department officials were on the plane with them.

Pakistan's Foreign Ministry spokesman Nafees Zakaria said the Pakistani raid that led to the family's rescue was based on a tip from US intelligence and shows that Pakistan will act against a "common enemy" when Washington shares information.

After the release, US President Donald Trump, who previously warned Pakistan to stop harbouring militants, praised Pakistan for its willingness to "do more to provide security in the region".

The rescue 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".

In the written statement, Mr Boyle expressed disagreement with US foreign policy.

"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.

Sorry, this video has expired Pakistan rescues Canadian, American couple and their three children from 'terrorist custody'

Mixed reactions from parents of captives

Mr Boyle's family thanked "everybody for all their prayers and good wishes" in an interview with the Toronto Star.

"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.

Sorry, this video has expired Parents grateful for couple's rescue in Pakistan

Ms Coleman's mother Lynda told ABC America hearing her daughter's voice for the first time was "incredible".

But her father Jim told ABC America he was still angry at Mr Boyle for arranging the trip to Afghanistan.

"Taking your pregnant wife to a very dangerous place, to me, and the kind of person I am, is unconscionable," he said.

A US military official said that a military hostage team had flown to Pakistan on Wednesday prepared to fly the family out.

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US officials had earlier told reporters, on the condition of anonymity, that Mr Boyle refused to board a US military aircraft in Pakistan.

Mr 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.

But speaking to reporters in Canada, Mr Boyle said "I assure you I have never refused to board any mode of transportation that would bring me closer to home."

Jim Coleman told ABC America "if it were me, and I saw a US aircraft, US soldiers, I'd be running for it."

Mr Boyle was once married to Zaynab Khadr, the older sister of former Guantanamo Bay detainee Omar Khadr and the daughter of a senior Al Qaeda financier.

Officials had discounted any link between that background and Mr Boyle's capture, with one official describing it in 2014 as a "horrible coincidence".

The US Justice Department said neither Mr Boyle nor Ms Coleman is wanted for any federal crime.

US officials call the Haqqani group a terrorist organisation and have targeted its leaders with drone strikes.

The group also operates like a criminal network, and unlike the Islamic State group, it does not typically execute Western hostages, preferring to ransom them for cash.

ABC/ wires