A freed Canadian hostage accused his kidnappers of murdering his infant daughter and raping his wife during his family's years-long captivity by the Haqqani network, a Taliban-affiliated group operating in Afghanistan and Pakistan.

Joshua Boyle leveled the accusations in a terse statement he read on his arrival in Toronto yesterday with his American wife, Caitlan Coleman, and three children, who were freed Wednesday by Pakistani troops.

He condemned the Haqqani network's "stupidity and evil of authorising the murder of my infant daughter" in "retaliation for my repeated refusal to accept an offer that the miscreant of the Haqqani network had made to me, and the stupidity and evil of the subsequent rape of my wife".

The Haqqani group is headed by Sirajuddin Haqqani, who is also the Afghan Taliban's deputy leader.

The faction has long been suspected of having links with Pakistan's shadowy military establishment.

Providing few details, Mr Boyle said the death of his daughter and his wife's rape occurred in 2014.

That was two years after he and Coleman, then "heavily pregnant," were kidnapped in a remote Taliban-controlled area of Afghanistan.

He said they were in Afghanistan as "pilgrims" helping poor villagers when they were captured.

The three children who survived the ordeal were all born in captivity.

"Obviously it will be of incredible importance to my family to build a secure sanctuary to call a home, to focus on edification and to regain some portion of the childhood they have lost," he said.

The Canadian government welcomed the family's arrival.

"Today, we join the Boyle family in rejoicing over the long-awaited return to Canada of their loved ones," the foreign ministry said in a statement.

"Canada has been actively engaged on Mr Boyle's case at all levels, and we will continue to support him and his family now that they have returned," it said, asking that the family's privacy be respected.

The Pakistani forces that freed the family said they acted on information received from the US intelligence services.

In his statement in Toronto, Mr Boyle denied he had refused a return trip aboard a US military aircraft.

He chose to fly back from Islamabad to Canada on commercial airlines via London.