Esmaili also said around 30 people had been arrested in the protests over the air disaster.
In his speech Rouhani called the downing of the Ukrainian plane by the Revolutionary Guard last week an "unforgivable error" and demanded that the Judiciary should appoint a "special court presided by a high-ranking judge and with tens of experts" to probe it.
A full picture of protests inside Iran is hard to obtain because of restrictions on independent media. But videos uploaded to the internet showed scores, possibly hundreds, of protesters on Monday at sites in Tehran and Isfahan, a major city south of the capital.
Anti-government protests ended entered a third day yesterday with dozens of demonstrators chanting slogans at a Tehran university.
Images emerged from the previous two days of protests showing wounded people being carried and pools of blood on the ground, while the sound of gunfire could be heard.
Iran's police denied firing at protesters.
And one of Iran's most famous actresses, Taraneh Alidoosti, posted that Iranians were being treated not as citizens but as "hostages".
Echoing what Iranian officials have said, Trudeau said the dozens of Canadian crash victims would be "home with their families" but for the tensions started by the United States killing of Qassem Soleimani. His statement on the judiciary's website did not say how many individuals had been detained or name them.
Trudeau said he has spoken with U.S. President Donald Trump on the need to de-escalate tensions in the region and noted that Washington gave Canada no advance notice of its strike against Gen. Qassem Soleimani, which set in motion Iran's missile strikes against coalition forces in Iraq, including Canadian personnel.
Charles Adler, a popular Canadian conservative talk-radio host, would not let Tehran or Washington off the hook.
Tehran had for days denied Western claims based on United States intelligence that the Boeing 737 had been downed by a missile.
The captain of the national men's volleyball team, Said Marouf, wrote on Instagram about "oppression" in Iran.
Stressing that "the government is accountable to Iranian, other nations who lost lives in plane crash".
Soleimani was Iran's second-in-command and the architect of its campaign to expand influence across the Middle East.
"If we had said straight away that they had shot it down, I am not sure they would have let us go to the wreckage at all, let us do what we were doing", he said.
"Death to the dictator", other footage showed protesters shouting, directing their fury directly at Ayatollah Ali Khamenei, Iran's supreme leader since 1989.
Reuters could not immediately verify the footage.
Video posts on January 14 showed scores gathered peacefully at two Tehran universities.
Police in Tehran have denied that shots were fired at protesters and said officers were given orders to "show restraint".
Despite Iran's contention that it was an accident, Fox said the investigators are keeping every option on the table.
Elsewhere in the Middle East, where Iran has wielded influence through a network of allied movements and proxies, governments that include powerful Iran-sponsored armed factions have faced months of hostile demonstrations in Lebanon and Iraq.