Cyprus is probing whether Helios airlines should have been granted an operating permit when it was set up in 1999.
One of the company´s jets crashed near Athens a week ago with the loss of all 121 people on board – the worst air disaster in Greek history.
The investigation comes after press reports suggested that the international body which oversees air transport, the ICAO, was against the previous Cypriot government´s decision to give Helios a license.
The ICAO apparently had doubts about the carrier and about the legislation in place to monitor it.
The company´s two other Boeing 737´s are currently in Sweden for comprehensive safety checks.
It is thought last Sunday´s crash happened after a sudden depressurisation problem knocked out the captain and the co-pilot.
The crew had apparently reported difficulties with the plane´s air conditioning system earlier in the flight.