Iran has a policy of filtering online content, which leaves popular websites such as Facebook, Twitter and YouTube inaccessible without the use of illegal software.
"After the order given by the head of the judicial authority, you have one month to take technical measures to ban and to monitor" Viber, Tango and WhatsApp, Gholamhossein Mohseni-Ejeie, the second-ranking member of Iran's judiciary, said in a letter to Telecommunications Minister Mahmoud Vaezi.
In the letter published by local news agencies on yesterday, he stressed that the messages constitute "crimes".
Local media said similar messages had been sent through the applications about current officials in the Iranian government, including supreme leader Ayatollah Ali Khamenei.
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If the telecommunications ministry does not take the measures the judiciary will intervene to "ban the social networks that have criminal content," Mohseni-Ejeie said. The ministry did not immediately react to the letter.
Conservatives have accused "counter-revolutionary groups" of circulating the "insults" under the guise of jokes.
Iranian President Hassan Rouhani has been calling for greater social freedoms in the country. Tehran's decision to approve faster 3G mobile Internet licences for two Iranian companies last month was seen as a first step toward making Internet access easier.
But the licenses decision caused controversy with conservative clerics and officials arguing that video call functions on smartphones could expose youngsters to "immoral content".
WhatsApp is a mobile messaging application available that allow users to swap text, picture and video messages. Viber and Tango let users call other people who have the applications installed on their mobiles.