Earlier on Tuesday, US warned of threats to commercial vessels in and around the Gulf in the wake of its confrontation with Iran.
All 176 people on board, including 57 Canadians and more than 80 Iranians, died when the plane crashed near Tehran following the missile strike.
Iran's president also called the Revolutionary Guard Corps' (IRGC) admission that it shot down the plane a "first good step" towards ensuring the matter is properly dealt with.
The extent of the unrest is hard to assess because of limits on independent reporting.
Separately, on Tuesday Iranian President Hassan Rouhani called for the formation of a special court to investigate the incident.
Judiciary spokesman Gholamhossein Esmaili said that "extensive investigations have taken place and some individuals have been arrested" for their role in the crash. The Canadian Press has independently confirmed at least 86 victims with ties to Canada, many of them students and professors returning after spending the December break visiting relatives in Iran.
Mr. Ismaili, the judiciary spokesman, said about 30 people have been arrested over the recent days of protests.
"We will not allow anyone to deface the country's security", Mr. Ismaili said.
The Canadian Transportation Safety Board "cannot confirm" the location of the flight records from Ukraine International Airlines Flight 752.
The shootdown and subsequent unrest comes amid one of the biggest escalations in tensions between Tehran and Washington since 1979.
Zelensky and Trudeau also discussed "further co-ordination of efforts to ensure proper global legal liability of those responsible for the plane crash", according to a more detailed Ukrainian government account of their call - their third in a week.
The domestic unrest triggered by the plane crash comes just two months after the most violent crackdown on protests since the revolution.
Other posts showed police in riot gear hitting protesters with batons on the street, the agency reported. Gunfire has also been heard, although police have denied shooting at protesters. The revelation has spurred large anti-government protests in the capital, Tehran, over the past three days, as well as demonstrations in other cities.
British Prime Minister Boris Johnson said on January 14 he was glad Iran had identified the downing of the plane as an "appalling mistake" and added that it was important the bodies of the British victims are now repatriated.
She said that, so far, there's been no need to send Canadian identification investigators to the crash site in Iran.
Ukraine's foreign minister said "grieving nations", five of the countries whose citizens were killed when an airliner was shot down, would meet on Thursday.
Iran's government was already reeling from the reimposition of sanctions by the United States, which quit an agreement with world powers under which Tehran would secure sanctions relief in return for scaling back its nuclear programme.
"The US makes its determinations". Trump officials have also maintained that they took action after learning Soleimani was planning "imminent" attacks on US personnel in the Middle East.