Nineteen people were 'martyred' in the friendly-fire incident, the ISNA news agency said, while another 15 were admitted to hospital in a 'good condition'.
Iranian media denied earlier reports that the Konarak had sunk, saying the vessel was towed away for inspection afterwards.
The Konarak had been overhauled in 2018 and was able to launch sea and anti-ship missiles but was not actively participating in the drill, state outlets said.
The Dutch-made, 155ft vessel was in service since 1988 and had capacity of 40 tons.
The friendly fire incident happened on Sunday near the port of Jask, some 790 miles southeast of Tehran, in the Gulf of Oman, state TV said.