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 died in a “natural” miscarriage.

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

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

“From the beginning up to their freedom, the wife and the husband were not separated even for a few minutes — and the reason for that was to avoid any suspicions,” the spokesman said by telephone.

When Coleman was about to deliver the child, Mujahid said, there were no doctors in the area where they were being held.

“One female child was naturally miscarried,” Mujahid said. “No one has intentionally killed the child or carried out any other abuse on them. If that was our plan, they would not have gone home with three children.”