Addressing the media here on Saturday, Trudeau said he told Rouhani that Iran's admission was an important step in providing answers for families, but more must be done, reports Xinhua news agency.
"A full and complete investigation must be conducted," Trudeau said.
"We need full clarity on how such a horrific tragedy could have occurred."
During their conversation, Rouhani promised further investigation into the circumstances surrounding the plane crash.
Rouhani said that the investigation by the Iranian military found that the missiles that caused the downing of the plane were fired due to "human error".
He said Iran welcomes any international cooperation in the framework of international regulations to shed more light on the incident.
The talks comes after Iran's Islamic Revolutionary Guard Corps (IRGC) admitted earlier on Saturday that one of its missiles had downed the Kiev-bound Ukraine International Airlines (UIA) flight PS75 on January 8.
It said Iran was on "high alert" that day because of the US threats of possibly hitting 52 spots in the country, the operator of the missile launch site was concerned about a possible "US cruise missile".
The passenger plane was mistaken for a "US cruise missile".
The crash occurred on the same day Iran launched more than a dozen ballistic missiles at two US military bases in Iraq, in retaliation for the killing of Iranian Major General Qasem Soleimani in an American drone attack in Baghdad on January 3.
( With inputs from IANS )