The ministry's director general of information applications, Samuel Abrijani Pangerapan, said it was preparing for the complete shutdown of Telegram in Indonesia if it does not come up with methods to block the unlawful content.
"I am personally a big fan of Indonesia - I've been there a few times and have many friends there".
Suspected militants arrested by Indonesian police recently have told authorities that they communicated with each other via Telegram and received orders and directions to carry out attacks through the app, including from Bahrun Naim, an Indonesian with the Islamic State group in Syria accused of orchestrating several attacks in the past 18 months.
The government has tipped an outright ban on social media networks as part of a crackdown on radicalisation and communications among terrorists and criminals online.
Durov, however, said he was "unaware" of requests made by the country earlier for it to remove the channels, calling it a "miscommunication".
It said in a statement that numerous app's public channels contained radical propaganda and terrorism-related content.
On Sunday, Durov reiterated that Telegram is heavily encrypted and privacy-oriented.
"The KDN's (Home Ministry's) observation, especially by the Anti-Terrorism Unit and the Special Branch of the Royal Malaysia Police (PDRM), find that the application (Telegram) has so far not been used in matters related to crime or for recruiting or raising funds for terrorism activities", Zahid said.
"We are forming a dedicated team of moderators with knowledge of Indonesian culture and language to be able to process reports of terrorist-related content more quickly and accurately", he said.
Telegram had previously responded to terrorism-related concerns in a May blog post.
Ahmad Zahid was asked to comment on the Indonesian government's action on Friday (July 14) to block the Telegram application following revelation that it was used to spread Daesh's ideology for violent activities.
Durov said Telegram blocks thousands of ISIL-related channels a month and is "always open to ideas on how to get better at this".
All of the reported channels by the Ministry of Communication and IT of Indonesia have been blocked.
Founded in 2013 by Russian brothers Nikolai and Pavel Durov, the application is a free messaging service that can be used as a smartphone app and on computers through a web interface or desktop messenger.
Indonesia has faced several terror attacks over the past year.