Rescue workers carried survivors on stretchers out of the gutted craft, which lay in a pool of water near the runway. In footage shown on the Iranian television, the middle section of the plane was charred and the roof collapsed, while firefighters sprayed the engines with water.
"The plane was shaking badly during the landing, then it suddenly lurched to the left," one survivor, Sahar Karimi, told The Associated Press by telephone from a hospital in Mashhad.
"Then it caught fire, and all the passengers rushed to the emergency exit," she said.
The spokesman for Iran's Civil Aviation Organization, Reza Jafarzadeh, said it was still not known what caused the plane to slide off the runway.
State television reported that a tire exploded as the plane landed, but Jafarzadeh said investigators had still not confirmed that. "Fortunately, the crew memebers are safe, and this can help the investigation team to reach its conclusions sooner," he said.
The flight by Iran Airtour, which is affiliated to Iran's national air carrier was arriving in Mashhad from Bandar Abbas on Iran's southern coast when the accident occurred.
The plane slid off the runway, "then its left wing hit the ground and caught fire," civil aviation chairman Nourollah Rezai Niaraki said in a television interview.
He said 29 passengers were killed, correcting an earlier television report of 80 dead.
The craft was a Russian-made Tupolev Tu-154, the same make as a passenger jet owned by Russia's Pulkovo Airlines that crashed in Ukraine on Aug. 22 while en route from a Russian resort to St. Petersburg, killing all 170 people on board.
In 2002, a Russian-made Tupolev-154 also run by Iran Airtour crashed in the mountains of western Iran, killing all 119 people on board.
Mashhad, located 1,000 kilometers (620 miles) northeast of Tehran, is visited by some 12 million people annually on pilgrimage to its Shiite Islamic shrines. It was not clear, however, if the passengers in Friday's flight included pilgrims.
Iranian President Mahmoud Ahmadinejad issued condolences to the families of the victims, while state radio read off the names of hospitals where the injured had been taken.
Iran has frequent air accidents, blamed on its aging fleet of aircraft and poor maintenance. In the deadliest recent crash, 110 people were killed in December when a military transport craft hit a building near Tehran's airport.
The country often blames U.S. sanctions that it says make it difficult to import spare parts, even from Europe. However, it does not have similar difficulty buying parts for its Russian planes.
The West offered to open the door to sales of new planes and spare parts in an incentive package aimed at getting it to roll back its nuclear program.
Iran's 13 airlines have 120 planes, averaging about 16 years old. Iran Airtour has 12 Tupelovs.
The country's main carrier, Iran Air, has seven Tupolevs among its 43-plane fleet. It also has seven are Boeings that were bought before the 1979 Islamic revolution, as well as 28 European Airbus and Fokker planes.
In March, Iran Air expressed interest in purchasing U.S. aircraft although it wasn't clear how it would circumvent U.S. sanctions in place since 1979, when diplomatic relations were cut after militants stormed the U.S. embassy and held hostages for more than a year.
The TU-154 is known for a poor safety record compared to comparable Western craft, the Boeing 727 or the Airbus 320.
The TU-154 the workhorse of passenger airlines in the former Soviet Union, has been in commercial service since 1972. More than 900 have been built and more than 160 exported to airlines around the world, particularly in former Soviet-bloc countries and Iran. Due to noise and pollution regulations, the planes do not fly to Western destinations.
Since the mark was introduced, 62 of its planes have been damaged in crashes or hard landings the deadliest in 1984, when a Tupolev landing at an airport in eastern Siberia smashed into cleaning vehicles left on the runway, killing 174 people.
In contrast, about 5 percent of the 1,800 727s built by Boeing have been involved in crashes, and one percent of the 1,400 Airbus 320s.