It was not immediately clear what caused the crash.
"Heavy snow is making it hard for rescuers to find the site of the crash", a television reporter accompanying rescue teams told state television.
Iran's Supreme Leader Ayatollah Ali Khamenei and President Hassan Rouhani expressed their condolences to the victims and their families, ordering officials to spare no efforts in their rescue operation, the state-run Islamic News Agency reported. Tabatabai said the plane had crashed into Mount Dena, which has an elevation of about 14,500 feet.
State TV said nobody had yet managed to reach the scene. The airport itself is at almost 6,000 feet.
Emergency service personnel and a rescue helicopter search for the plane that crashed in a mountainous area of central Iran, on Monday.
Aseman Airlines operates mainly domestic routes in Iran, but also runs global routes.
The other 190 airlines banned by Europe were blacklisted due to broader concerns over safety oversight in their respective countries.
It was carrying 59 passengers and 6 crewmembers.More news: U.S. routs Slovakia to reach Olympic men's hockey quarter-finals
An ATR-72 - the same model involved in Sunday's crash. Aseman Airlines posted about the plane on Instagram in October of last year, saying that after being grounded for seven years, it was being repaired, tested and reinstated.
The plane, a 20-year-old ATR-72 flown by Iran's Aseman Airlines, left Tehran at around 5 a.m.
Earlier reports said there were 66 people on board. The search for the Aseman Airlines flight has been impeded by glacial temperatures and mountainous terrain.
Decades of global sanctions have left Iran with an ageing fleet of passenger planes which it has struggled to maintain and modernise.
Following the 2015 landmark nuclear deal with world powers, Iran signed deals with both Airbus and Boeing to buy scores of passenger planes.
Iran has suffered a series of major airplane crashes in recent decades.
Emergency personnel have reached the crash zone via land and are still looking for plane's wreckage. The first few Airbus jets have already arrived in Tehran.
Pilot Hojatollah Fooled successfully landed a similar plane after an engine problem in 2013, the airline said in an Instagram post.