There have since been reports, so far unverified, that Mr. Azari Jahromi has resigned.
On Tuesday, some users of Telegram in Iran said they were still able to communicate through the app over their home internet connections. In the confusion, several websites that are usually freely accessible — including Wikipedia and Google — were hard to reach.
Iran is not the only country trying to block Telegram. Two weeks ago, Russia obtained a court order to shut down the service after its founder, Pavel V. Durov, refused to provide the security services with the keys to read users’ encrypted messages.
In Iran, the battle over the app has become something of a litmus test for Mr. Rouhani, whose popularity has dropped significantly since his re-election in May last year. During his campaign, he promised to deliver more freedoms, to provide greater employment opportunities and to get the country’s notorious morality police off the streets. He has largely fallen short of those goals.
“Mr. President, none of your promises were realized, and preventing Telegram from being blocked is your last stronghold,” a journalist named Nahid Molavi wrote on Twitter.
Telegram is widely used in Iran, for activities as varied as chatting, booking appointments at beauty salons, selling cars or finding partners. Even the supreme leader, Ayatollah Ali Khamenei, had his own channel until recently. Such channels, which sometimes draw hundreds of thousands of users who receive instant messages at the push of a button, played a major role in spreading videos of nationwide protests in December.
On Monday, Iran’s judiciary issued a decree ordering internet service providers to block access to the Telegram app, as they have already been doing for years for Facebook and Twitter.
In recent weeks, government institutions had already begun taking down their Telegram channels, urging people to switch to Iranian applications such as Soroush. But many Iranians chose not to follow the guidance.