State television described the missile strike as an accident during a training exercise, saying the Konarak had remained too close to the target. The Konarak had been putting targets out in the water for other ships to fire upon, it said.
An Iranian missile that struck a support ship in a friendly-fire incident has killed 19 sailors and wounded 15 others, Iran's navy said in a statement on Monday.
The friendly fire incident happened during a naval exercise on Sunday near the port of Jask, some 1,270 kilometres (790 miles) southeast of Tehran, in the Gulf of Oman, state TV said.
The missile struck the Konarak, a Hendijan-class support ship, taking part in the exercise.
State television described the missile strike as an accident, saying the Konarak had remained too close to the target. The Konarak had been putting targets out in the water for other ships to fire upon, it said.
A local hospital admitted 12 sailors and treated another three with slight wounds, the state-run IRNA news agency reported.
Iranian media said the Konarak had been overhauled in 2018 and was able to launch sea and anti-ship missiles. The Dutch-made, 47-metre (155-foot) vessel was in service since 1988 and had capacity of 40 tons. It usually carries a crew of 20 sailors.
Iran regularly holds exercises in the region, which is closed to the strategic Strait of Hormuz, the narrow mouth of the Persian Gulf through which 20 percent of the world's oil passes. The US Navy's 5th Fleet, which monitors the region, did not immediately respond to a request for comment.
Iranian media rarely report on mishaps during its exercises, signaling the severity of the incident.
This incident also comes amid months of heightened tensions between Iran and the US since President Donald Trump unilaterally withdrew from Tehran's nuclear deal with world powers in 2018 and imposed crushing sanctions on the country.
It also comes in the wake of a flurry of activity in the Persian Gulf in recent weeks.
Late last month, there was a dangerously close confrontation between US Navy vessels and Iranian Navy boats close to Iranian territorial waters in the Gulf.
Later, the US Navy issued a statement, accusing the Iranian Navy of harassment.
US President Donald Trump took to Twitter, saying he had instructed the US Navy to shoot down and destroy Iranian gunboats if they harass US ships.
In response, IRGC chief Major General Hossein Salami said Iranian naval forces have been ordered to target any US vessel or warship in the Persian Gulf if they harass Iranian vessels.
On Saturday, there was a rumour that a US drone had been downed in Iranian territorial waters, which later proved to be a hoax.
The latest incident comes as military exercises have intensified in the Persian Gulf region, which shows the Iranian military is taking the US threats seriously.