"The 7908 Caspian flight crashed 16 minutes after its take-off from the International Imam Khomeini Airport," Iranian Aviation Organisation spokesman Reza Jafarzadeh said, reported Iran's Press TV.
He said no problems were reported before take-off and there would be a full investigation into the cause of the crash.
At Yerevan's airport, one woman wept as she said her sister and two nephews, aged six and 11, had been on the flight.
"What will I do without them?" said Tina Karapetian, 45, before collapsing.
It was earlier reported that most of the passengers were Armenian, but officials later said the majority on board were Iranian.
A Caspian Airlines spokesman told Reuters news agency up to 25 of the passengers were Armenians.
There were also two Georgians on the plane, which had 153 passengers and 15 crew.
One witness said the Tu-154 circled briefly looking for an emergency landing site, while another said the plane's tail was on fire.
A man who saw the crash said the aircraft exploded on impact.
Jon Leyne, BBC News
Iran has a notoriously bad air safety record. Because of sanctions imposed by the United States, Iran relies on an increasingly ageing fleet of airliners, and has trouble buying spares.
There are tales of aircrew buying spare parts on flights to Europe, then sneaking them back to Iran in the cockpit. While those sanctions don't apply to aircraft from Russia and Ukraine, many planes from those countries in the Iranian fleet also appear well past their best.
For some people, flying in Iran can be a nerve-wracking experience. Stepping on board, it often becomes quickly apparent you are in a plane that has done many years service.
There are also frequent delays because of the shortage of aircraft. Iranian engineers and aircrew do their best to keep their fleets in service.
"I saw the plane crashing nose-down. It hit the ground causing a big explosion. The impact shook the ground like an earthquake. Then, plane pieces were scattered all over the fields," 23-year-old Ali Akbar Hashemi told AP news agency.
Eight members of Iran's national junior judo team and two coaches were on the flight, heading for training with the Armenian team.
Mohammad Reza Montazer Khorasan, the head of the disaster management centre at Iran's health ministry, said: "All people aboard... the crashed plane are dead," according to AFP news agency.
Television footage showed a massive crater in a field, with smouldering debris over a wide area.
The Qazvin Fire Department Chief said: "The area of the disaster is very wide and wreckage of the crashed plane has been thrown around as far as 150 to 200m."
Iranian President Mahmoud Ahmadinejad offered his condolences to the families of the victims.
IRANIAN PLANE CRASHES
Feb 2006: Tupolev crashes in Tehran, kills 29 people
Dec 2005: C-130 military transport plane crashes near Tehran, kills 110
Feb 2003: Iranian military transport plane crashes in south of country, kills all 276 on board
Dec 2002: Antonov 140 commuter plane crashes in central Iran, kills all 46 people on board
Feb 2002: Tupolev crashes in west Iran, kills all 199 on board
It was the third deadly crash of a Tupolev Tu-154 in Iran since 2002.
The BBC's Jon Leyne says Iran's civil and military air fleets are made up of elderly aircraft, in poor condition due to their age and lack of maintenance.
Since the Islamic revolution of 1979, trade embargoes by Western nations have forced Iran to buy mainly Russian-built planes to supplement an existing fleet of Boeings and other American and European models.
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