The crash of the Ukraine International Airlines flight near Tehran killed 176 people, including 138 who were bound for Canada.
France's BEA air accident agency said it would be involved in the investigation.
He said would discuss the investigation with US Secretary of State Mike Pompeo later today.
"When families lose loved ones, they deserve to know what happened".More news: Oscars: Saoirse Ronan receives fourth Academy Award nomination
He also said Iran may request help from global experts if it is not able to extract the recordings from the "black boxes".
An Iranian official denied a missile hit the plane and called on both the United States and Canada to release data backing their allegations.
But Iran's aviation authority chief said the missile theory could not be "scientifically correct" because it was not possible for an airliner to be hit and "continue flying for 60 to 70 seconds".
It is Iran's worst civil aviation disaster since 1988 when the USA military said it shot down an Iran Air plane over the Gulf by mistake, killing all 290 people on board.
A United States official, citing satellite data, said Washington had concluded with a high degree of certainty that anti-aircraft missiles brought down the plane in error.More news: Gwyneth Paltrow is selling a candle that smells like her vagina
The New York Times said it had obtained a video appearing to show an Iranian missile hitting a plane near Tehran airport.
Shevchenko emphasized that no final decision was made on that important point and said more discussions are planned, although Ukrainian media reported late Thursday that Rouhani had assured Zelensky that Ukrainian investigators will be provided access to all the necessary data.
That tragedy that came just hours after Iran fired more than a dozen ballistic missiles at two airbases in Iraq housing US and coalition troops - in direct retaliation for the Trump administration's targeted killing of Iranian Revolutionary Guard commander Gen. Qassem Soleimani just days earlier.
One US official cited by Reuters said US satellites had detected the launch of two surface-to-air missiles shortly after the Boeing 737-800 left Tehran.More news: Shane Warne wants five-match India-Australia Test series in next cycle