Two others were injured in the crash, which occurred shortly after the plane took off from an airport in Tehran, bound for Shiraz, about 1,000 kilometers to the south, the TV said.
The plane, an Antonov-74, suffered a "technical failure in its engine," the commander of the Revolutionary Guards, Gen. Yahya Rahim Safavi, told the official Islamic Republic News Agency.
"Some 30 members of the elite Revolutionary Guards and six crew members were killed in the crash while they were heading for a military site in southern Iran," state-run television said, reading a statement from the Guards. The crew were also guardsmen.
Earlier, the television had said the number of victims was 38. It did not give any details on the names or ranks of the victims of the crash -- the third military air plane crash in the last year.
Another official, Gen. Eskandar Moemeni, a deputy police chief, told reporters that the number of dead had increased to 39 after three injured people died in a hospital.
There was no immediate way to determine which number was accurate.
The two survivors were admitted to hospital, the Islamic Republic News Agency reported, without giving their condition.
An investigation has been launched, IRNA added.
In January, a small military passenger Falcon jet crashed in northwestern Iran, killing the commander of the ground forces of the elite Revolutionary Guards. That happened just one month after a military transport, a U.S.-made C-130 plane, crashed into a 10-story building near Tehran's Mehrabad airport, killing 115 people.
In Iran, the Revolutionary Guards are a separate organization from the regular armed forces. Founded after the 1979 Islamic Revolution, the Guards have their own air, naval and ground components. President Mahmoud Ahmadinejad is a former commander in the Guards.
Iran has a history of aircraft accidents involving a heavy loss of life. The government has blamed a U.S. trade embargo, which makes it impossible for Iran to buy parts for its old U.S.-built aircraft. But critics have also said planes are poorly maintained.