The commandos fired at the suspect after he shot at them when they asked him to surrender, army Major General Motiur Rahman told reporters, according to ATN TV news.
He said that the suspect was carrying a pistol, but did not say where the shooting took place.
The army official said the suspect, whose name has not been released, asked to speak to his wife and to Prime Minister Sheikh Hasina. The suspect died before reaching the hospital, he said.
The suspect appeared to be "mentally imbalanced," said Air Vice-Marshal M. Naim Hassan, chairman of the Civil Aviation Authority. "I am saying this because of his behaviour. He wanted to talk to the prime minister."
Before the suspect was pronounced dead, Rahman, had described him as a "terrorist" and said that he had been arrested and was being questioned.
Bangladeshi soldiers could be seen during the live TV broadcast taking positions inside Shah Amanat International Airport in Chittagong, 252km southeast of Dhaka.
- AP