The insurgents, who control or influence about half of Afghanistan, also accused the WHO of "suspicious movements" during a vaccination campaign.
As a result, the Taliban has "decided to ban the operation of these two organisations across the country until further notice," the militants said, noting they would not guarantee health workers' safety.
"We acknowledge this announcement and have suspended our activities in the country due to the withdrawal of security guarantees," Waudo told AFP.
"Therefore, we are now in the process of contacting the (Taliban) to initiate a bilateral and confidential dialogue in view of the statement."
The WHO did not immediately respond to requests for comment.
The Taliban last August cancelled a "security agreement" with the ICRC, which suspended activities as a result.
According to the Taliban, the ICRC resumed its activities in October following talks.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)