Iran has signalled that Canada's Transportation Safety Board (TSB) will play a more active role than international rules require in the investigation of the Iranian military's shooting down of a Ukrainian airliner last week, according to the agency's head, Kathy Fox.

A missile fired by Iran brought down the Ukrainian airlines plane on January 8 killing all 176 on board, including 57 Canadians. The incident, which Tehran has said was unintentional, came just hours after Iran fired missiles at two Iraqi bases housing US soldiers in retaliation for the US drone-strike killing of Iranian military commander Qassem Soleimani last week.

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"In this investigation - and I want to be clear about this - we do not yet fully know what the scope of our role will be," Fox said in a news conference on Monday in Ottowa.

She added that "there have been early signs that Iran is allowing the TSB to play a more active role than normally permitted", including by inviting its investigators to participate in downloading and analysing the data in the cockpit voice and flight data recorders "whenever and wherever that takes place".

Canada has been invited to participate in the probe because a large number of its citizens were involved, but according to international rules, Iran leads the investigation.

Fox added that Canada's investigation will pose questions that will be "very uncomfortable" for Iran.

One of the central questions is why Iran did not shut down the airspace around Tehran given the tensions created by Iran's missile attack on the Iraqi bases earlier in the day, the TSB's director of investigations, Natacha Van Themsche, said during the press briefing.

On Sunday, the TSB said it had obtained visas for two of its investigators to travel to Iran.

A second team of investigators who specialise in aircraft recorder download and analysis will be deployed once TSB confirms where and when that activity would take place, the agency said.

Van Themsche added that Iran has said it will allow the Canadian investigators to examine the remains of the wreckage.