Footage shows the aircraft heading towards the ground at high speed with its landing gear down, before bursting into flames as it lands.
The airline said the plane “made an emergency landing” about 3km (1.9 miles) from Aktau.
It took off from the Azerbaijani capital Baku at 03:55 GMT on Wednesday, and crashed around 06:28, data from flight-tracking website Flightradar24 showed.
Reports from Russian media say the aircraft collided with a flock of birds before crashing, but this has not yet been confirmed.
Officials from the countries involved have stated different numbers for those who were on board and for those who survived.
The airline said 62 passengers and 5 crew members were on board the Embraer 190 but other reports put the total at 72. The reported number of survivors ranges from 28 to 32.
Those on board were mostly Azerbaijani nationals, but there were also some passengers from Russia, Kazakhstan, and Kyrgyzstan.