State television earlier showed the battered black boxes, saying their information could be downloaded and analyzed.
There were 176 people on board the aircraft - 167 passengers (including two Ukrainians) and nine crew (all Ukrainians). Most of the victims of the Ukrainian plane crash in Tehran are citizens of Iran (82) and Canada (63).
The Foreign Office advice came as Western leaders said intelligence suggested the Ukrainian aircraft was mistakenly shot down by an Iranian missile amid escalating tensions between Iran and the US.
Iran has denied it is responsible for the plane crash, which it says was likely caused by a technical malfunction. Tehran blamed a technical malfunction while USA and Canadian authorities said Iran shot down the aircraft perhaps unintentionally.
The pilot did not call the tower because "he must have been trying to save the airplane before anything else", Abedzadeh said.
Canada's transportation safety board on said yesterday it had accepted an invitation from Iran's civil aviation authority to join the inquiry.
Earlier on Thursday a USA official, citing an extensive review of satellite data, said Washington had concluded with a high degree of certainty that anti-aircraft missiles brought the plane down.
Investigators are pursuing several possibilities, including engine failure, a missile strike or an act of terror.
As speculation about the cause grew, a senior advisor to President Hassan Rouhani warned Iranians working for Farsi-language media overseas to "not participate in the psychological warfare" against Iran over the plane crash.
The air disaster unfolded just hours after Iran fired 22 ballistic missiles at military bases hosting United States troops in Iraq in retaliation for the U.S. drone strike that killed Iranian military commander Qassem Soleimani in Baghdad last week.
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