Iran's telecoms minister said on Wednesday that Telegram would only be unblocked if it removed "terrorist" content after the social media app was shut down during this week's protests.
"I had mail exchanges with the head of Telegram and I told him that the continuation of Telegram's activities is conditioned on the suppression of terrorist content," Mohammad-Javad Azari Jahromi told state television.
"The organs of power welcome criticism on social media... but in the current climate, in particular on Telegram, there is propaganda for violent and terrorist actions," he added.
At 36, Azari Jahromi was the youngest-ever minister when he was appointed in August, and he had stated his opposition to the internet controls in place in Iran.
More than 41 million Iranians have smartphones in the country of 80 million, and at least 25 million use Telegram daily.
For many it has become the main source of news and a way of bypassing Iran's highly restrictive media environment.
The Iranian government blocked Telegram and Instagram on mobile phones soon after protests began across the country last Thursday.
US President Donald Trump tweeted that Iran "has now closed down the Internet so that peaceful demonstrators cannot communicate. Not good!"
Users were still able to bypass the restrictions using privacy software -- as they already do for blocked sites such as Twitter and YouTube -- although the internet was also slowed down in some areas, making access more difficult.
Azari Jahromi demanded on Sunday that Telegram remove a channel called Amadnews, which had around 1.4 million followers, that he said was inciting an "armed uprising".
Telegram removed Amadnews but CEO Pavel Durov refused to block other channels that had not advocated violence.
"Iranian authorities are blocking access to Telegram for the majority of Iranians after our public refusal to shut down (Sedaie Mardom) and other peacefully protesting channels," he said, referring to another channel accused by Iran of fomenting violence.
Azari Jahromi said restrictions would be lifted in "several days" if calm was restored on the streets of Iran.