The Taliban on Sunday rejected claims by freed Canadian hostage Joshua Boyle that his kidnappers had killed his child and raped his wife during the family's captivity, saying the woman had a "natural miscarriage".

Boyle and his American wife Caitlan Coleman were seized by the Taliban while hiking in Afghanistan in 2012. The couple and their three children born in captivity were freed on Wednesday in a Pakistani military operation triggered by US intelligence and are now back in Canada.

After landing in Toronto on Friday, Boyle had accused his captors of killing his baby daughter and raping his wife — accusations which the Taliban said were "fake".

In a statement read on his arrival, Boyle had 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".

Taliban spokesman Zabihullah Mujahid said Boyle and Coleman were never separated during their captivity, "precisely due to the fact that the mujahideen did not want to incite any suspicion", but he admitted a baby had died.

"During a period of detention an incident did take place when the woman became ill. The area was remote, no doctors were present and due to this severe condition, the woman had a natural miscarriage of a girl," Mujahid said in a statement.

"The allegations floating around in the media have nothing to do with the reality because the said people are now in the hands of our enemy."

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

Providing few details, Boyle had said that 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 the war-torn country as "pilgrims" helping poor villagers when they were captured.