The Aseman Airlines flight left Tehran's Mehrabad airport at around 0800 (0430 GMT) for the city of Yasuj in Isfahan province, said Mohammad Tabatabai, director of public relations for the airline.
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The plane crashed into Dena mountain, part of the Zagros range, around 23 kilometres (14 miles) from Yasuj, some 500 kilometres south of the capital, he told state broadcaster IRIB.
"After searches in the area, unfortunately we were informed that the plane crashed. Unfortunately, all our dear ones lost their lives in this incident," Mohammad Tabatabai, public relations director for Aseman Airlines, told state broadcaster IRIB.
The plane was carrying 60 passengers, including one child, as well as six crew, he added.
A helicopter sent by Iran's national emergency services was unable to land at the site of the accident due to severe weather, its spokesman said.
The Relief and Rescue Organisation of Iran's Red Crescent said it had dispatched 12 teams to the region.
"Given the fact that the area is mountainous, it is not possible to send ambulances," Mojtaba Khaledi, spokesman for the national emergency services, told ISNA news agency.
Decades of international sanctions have left Iran with an ageing fleet of passenger planes which it has struggled to maintain and modernise.
It has suffered multiple aviation disasters, most recently in 2014 when a Sepahan plane crashed killing 39 people.
Tabatabai said the plane that crashed on Sunday was a twin-engine turboprop ATR-72.
Aseman currently has a fleet of 36 planes - half of them 105-seat Dutch Fokker 100s.
Its three Boeing 727-200s are almost as old as the Islamic revolution, having made their first flights in 1980.
Lifting sanctions on aviation purchases was a key clause in the nuclear deal Iran signed with world powers in 2015.
Following the deal, Aseman Airlines finalised an agreement to buy 30 Boeing 737 MAX jets for $3 billion (2.4 billion euros) last June, with an option to buy 30 more.
However, the sale could be scuppered if US President Donald Trump chooses to reimpose sanctions in the coming months, as he has threatened to do.
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The US has maintained its own sanctions on Iran, which block almost all trade with the country, but plane manufacturers were given a specific exemption under the nuclear deal.
Boeing, which is also building 80 planes for national carrier Iran Air, faces heavy criticism from US lawmakers who say Iranian airlines have been used to ship weapons and troops to Syria and other conflict zones.
The US Treasury Department approved the sale of the 80 Boeing jets as well as 100 Airbus planes to Iran Air. The first few Airbus jets have already arrived in Tehran.
Condolences pour in for Iran plane crash
Israeli Prime Minister Benjamin Netanyahu on Sunday offered his condolences over Iranian plane crash, just moments after he launched a blistering attack on Tehran's government.
"I take this opportunity to send condolences to the families of the 66 civilians that lost their lives in the plane accident today," Netanyahu said at the Munich Security Conference.
"We have no quarrel with the people of Iran, only with the regime that torments them," he added.
Earlier in his fiery speech, the premier warned Tehran not to "test Israel's resolve" as tensions between the arch enemies have reached fresh heights over Iran's activities in Syria.
Israel fears that Iran, which is supporting Syrian President Bashar al-Assad's regime, is seeking to entrench itself militarily next door.
Punjab Chief Minister Shehbaz Sharif took to twitter to express his condolences.
Saddened by the news of an Iranian plane crash and loss of precious lives in it. I extend my sympathies and condolences to the leadership and brotherly people of Iran. Our thoughts and prayers are with the bereaved families at this difficult hour.
— Shehbaz Sharif (@CMShehbaz) February 18, 2018
Chief of Army Staff (COAS) General Qamar Javed Bajwa also condoled the loss of precious lives in the tragic plane crash.
He shared grief of bereaved families and brotherly Iranian nation, said DG ISPR Maj-Gen Asif Ghafoor in a tweet.
COAS condoles loss of precious lives in tragic Iranian plane crash. Shares grief of bereaved families and brotherly Iranian nation.
— DG ISPR (@OfficialDGISPR) February 18, 2018
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