KABUL, Afghanistan — The Taliban on Sunday denied an assertion by a freed Canadian hostage that his American wife had been raped during their five years of captivity and that their infant had been killed by the Haqqani network, a brutal arm of the Afghan insurgency.

The militants said the child had died during a miscarriage.

Soon after arriving in Toronto on Friday with his wife, Caitlan Coleman, and their three children, the former captive, Joshua Boyle, said she had been raped by members of the Haqqani network.

He also said the network had authorized “the murder of my infant daughter,” their fourth child. Ms. Coleman was pregnant when the couple were abducted in 2012 while traveling in Afghanistan.

Zabihullah Mujahid, a Taliban spokesman, rejected the accusations of rape as “fabricated claims” fed to Mr. Boyle.