The ATR-72 twin-engine plane, in service since 1993, disappeared from radar around 45 minutes after takeoff.
"The plane had 50 to 60 passengers", Pir Hossein Koolivand told the Fars news agency.
Emergency service personnel and a rescue helicopter search for the plane that crashed in a mountainous area of central Iran, on Monday.
Todd Curtis, founder of the website AirSafe.com said Iran was able to keep its planes flying despite sanctions that made it more hard to buy parts or new aircraft, but that the aviation sector was not able to benefit from working with others in the industry from around the world.
The wreckage of a plane that crashed in Iran on Sunday has been found, local media are reporting.
Anxious relatives of passengers gathered at Yasuj airport.
Supreme Leader Ayatollah Ali Khamenei offered his condolences and encouraged everyone involved "to heal the sorrow of the families and relatives of victims", according to the the IRNA news agency.
The President asked the transport minister to lead an investigation into the crash.
Aseman is a semi-private airline that specialises in flights to remote airfields in Iran and also flies to some global destinations.
A spokesman for ATR, which is part-owned by Europe's Airbus, told AFP "the circumstances of the accident remain unknown" and global investigators were ready to assist Iran "if needed".
The US Treasury Department, which must approve aviation sales to Iran, has done so for 80 Boeing jets and 100 Airbus planes for national carrier Iran Air. In February 2003, an Ilyushin-76 troop carrier crashed in southeast Iran, killing all 276 Revolutionary Guard soldiers and crew. The airline has retracted a statement saying definitively that all aboard were dead.
Aviation safety specialist David Learmount told Al Jazeera the crash was caused by a "failure of navigation".
Iran has not been able to renew its fleet of commercial aircraft under pro-longed global sanctions.
In April 2017, ATR sealed a $536 million sale with Iran Air for at least 20 aircraft. Aseman signed a deal a year ago to buy at least 30 Boeing 737 MAX jets.
Home to 80 million people, Iran represents one of the last untapped aviation markets in the world.
Aseman Airlines has suffered other major crashes with fatalities.
The Antonov 74 aircraft, headed to Shiraz in the south of Iran, crashed shortly after takeoff, the airport's director said.