Text messages from a phone number used by a Taliban spokesman had announced the death of the groups' commander Mullah Omar, but the reports were claimed to be fake.
Taliban spokesman Zabiullah Mujahid said leader Omar was alive and claimed his phone was "hacked".
He told CNN the reports were "just propaganda against our leader and our mission"
The groups' website was also allegedly hacked.
Mujahid and spokesman Qari Yousef Ahmadi denounced the attacks and claimed they were launched by a "cunning enemy" who had committed "technical larceny."
Mujahid told Reuters that it was the "work of American intelligence" and said it "will take revenge on the telephone network providers".
It said the group's technical team from "the Islamic Emirate's Information and Cultural Commission" were investigating the alleged hacks.