The messaging application also allows a group chat with more than 10,000 members without providing details, including phone numbers, to the group's administrator, a feature that Tito said would be useful for terrorists.
Samuel Pangerapan, the director general of informatics applications at the ministry, said they are preparing for the complete closure of Telegram in Indonesia if it does not develop procedures to block unlawful content.
"This has to be done because there are many channels on this service that are full of radical and terrorist propaganda, hatred, ways to make bombs, how to carry out attacks, disturbing images, which are all in conflict with Indonesian law", the communications ministry said in a statement on its website.
The country's Ministry of Communication and IT blocked the web-based version of the messaging service on Friday.
"Telegram is heavily encrypted and privacy-oriented, but we're no friends of terrorists - in fact, every month we block thousands of IS (Islamic State)-related public channels", the BBC quoted Duroy as saying.
Indonesians are among of the world's biggest users of social media.
Durov said Telegram has now blocked the channels that were reported to it by the Indonesian government.
Telegram is a free Russian-designed messaging app that lets people exchange messages, photos and videos in groups of up to 5,000.
Almost two months after the initial assault, Philippine forces are still battling to regain complete control of the city.
Zahid said monitoring by Malaysian authorities so far found no evidence related to crime or terrorism as far as Telegram was concerned.
"We are trying to support their business but we also need their cooperation in addressing our concerns i.e.in addressing negative content", he said.