Another 80 people were taken to hospital with injuries, mostly broken limbs suffered after jumping from the Boeing 707 when it came to a standstill.
Reza Jafarzadeh, a spokesman for Iran's Civil Aviation Organisation, said on Thursday that the bodies of two adults were found and that searches were under way for a four-year-old child.
The official IRNA news agency, citing passengers' accounts, said the child had fallen into a river near the runway and drowned during the chaotic evacuation of the aircraft.
The child's father told the Kayhan newspaper he had lost hold of his son while trying to save another child from drowning.
Another passenger, Maliheh Nezami, 30, told Kayhan she heard a loud explosion from the front of the plane shortly after landing.
"We saw fire coming out of both of the plane's engines and then it fell into the river"
"We saw fire coming out of both of the plane's engines and then it fell into the river," she said.
Black box retrieved
Jafarzadeh said officials had retrieved the aircraft's "black box" flight recorder, which would help identify the exact cause of the crash. All the injured have been released from hospital, he said.
State media have carried various accounts of how the plane operated by Saha Airlines, which is owned by Iran's armed forces, came to crash at the end of its journey from the Gulf island of Kish.
IRNA said a tyre had burst on landing while one state television channel said the plane had been unable to put down its landing gear because of a technical fault.
Hampered from buying new aircraft and spare parts because of US economic sanctions, Iran is plagued by frequent air crashes.