Montazeri, who heads the Committee for Determining Criminal Web Content, said the issue is beyond the competence of the Committee, Iranian media outlets reported.
Montazeri’s comment comes after six Iranian ministers and two MPs, who are members of the Committee, in a letter to him called for unblocking Twitter.
In the letter, the Committee members called on the prosecutor general for raising the issue in the Committee and removing the ban on Twitter.
The Committee for Determining Criminal Web Content, an Iranian cyberspace watchdog which makes decisions on blocking access to websites, was established in 2009.
The Committee has 13 members, including 6 ministers from Iranian President Hassan Rouhani's cabinet.
Iran’s Communications Minister Mohammad Javad Azari Jahromi, Education Minister Mohammad Bathaee, Intelligence Minister Mahmoud Alavi, Justice Minister Alireza Avayi, Science Minister Mansour Gholami, Culture Minister Abbas Salehi are the ministers who signed the letter.
Meanwhile, Montazeri said that Twitter was blocked based on a judiciary order, so the issue cannot be discussed in the Committee.
As long as Twitter's terms are the same as before, the judicial order for access ban will remain in place, he added.
The Iranian authorities banned Facebook and Twitter in the summer of 2009 when former president Mahmoud Ahmadinejad's disputed re-election victory sparked off massive protests that gained momentum with the help of organizers using social media.
Filtering doesn't mean Iranians are totally cut off from the world's most popular social networks. Visitors from Iran are able to log in both Twitter and Facebook via proxies, special IP addresses, which serve as hubs through which internet requests are processed.
Senior Iranian officials, including Supreme Leader Ayatollah Ali Khamenei, President Hassan Rouhani, Foreign Minister Mohammad Javad Zarif actively use the social media while it is blocked and illegal for the public.
Iran has recently blocked the popular messaging app Telegram as well. The application is used by an estimated 40 million users in the country, almost the half of the population, according to Iranian officials.
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