Ukraine International Airlines Flight 752 crashed near Tehran last Wednesday, just hours after the Iranian military fired multiple ballistic missiles into neighboring Iraq, targeting military bases housing American troops, in retaliation for the US airstrike that killed Iran's most powerful general.
A full picture of protests inside Iran is hard to obtain because of restrictions on independent media.
"The judiciary should form a special court with a ranking judge and dozens of experts", Rohani said in his speech, adding that the Iranian armed forces' admission in the incident was "a good first step".
"Extensive investigations have been carried out and some people have been arrested", said spokesman Gholamhossein Esmaili, confirming start of the judicial inquiry. His statement on the judiciary's website did not say how many individuals had been detained or name them.
"Around 30 people have been arrested for taking part in illegal gatherings".
Image copyright EPA Image caption A banner on a lamppost in Tehran says: "We are all in pain and sympathise".
He added that the global community has been "very, very clear about needing to have a non-nuclear Iran" but also in 'managing the tensions in the region that are brought about by USA actions as well'.
In an interview with Global National's Dawna Friesen on Monday, Trudeau spoke about the Canadian response to the plane crash, as well as holding Iran accountable in the investigation into how the missile that took down the plane was sacked.
The disaster and subsequent unrest comes amid one of the biggest escalations between Tehran and Washington since 1979.
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A woman attending a candlelight vigil Saturday to remember the victims of the Ukraine plane crash, talks to a policeman, at the gate of Amri Kabir University in Tehran, Iran, in photo released by Iranian Students' News Agency, ISNA.
Tehran for days denied Western claims based on U.S. intelligence that the Boeing 737 had been downed by a missile.
Previously, the Iranian side stated that the crash had been caused by technical problems.
Iranian authorities are accused of killing hundreds of demonstrators in a crackdown two months ago, in what was probably the worst anti-government unrest since the 1979 revolution. In Iraq and Lebanon, governments backed by pro-Iran armed groups have also faced mass protests.
"Death to the dictator", other footage showed protesters shouting, directing their fury directly at Ayatollah Ali Khamenei, Iran's supreme leader since 1989. Gunshots could be heard, although the police have denied opening fire.
Video posts on January 14 showed scores gathered peacefully at two Tehran universities.
After initially denying responsibility for the aircraft's downing, Iran's government has since said its military mistook the plane for an incoming hostile target.
Five nations whose citizens died in the crash, which killed all 176 people aboard, will meet in London on Thursday to discuss possible legal action, Ukraine's foreign minister told Reuters. We should assure people that it will not happen again'.
Prime Minister Justin Trudeau in part blamed the loss of life on heightened tensions between Iran and the USA following Washington's targeted killing of a prominent Iranian general.