Ammon News - It is the third naval disaster for Iran in recent years - 19 sailors were killed in 2020 in a training exercise in the same area, Sky reported.
Iran's largest navy warship has sunk in the Gulf of Oman after catching fire.
Iranian media did not give an explanation for the fire but said it had started at 2.25am local time on Wednesday, according to Sky.
Photos on social media showed sailors in life jackets evacuating the ship as it sank near the port of Jask, about 790 miles from the capital Tehran.
"All efforts to save the vessel were unsuccessful and it sank," said Iran's semi-official Fars news agency.
The ship was on a training mission, according to state TV.
It happened in an area where there have been accusations of attacks on ships owned by arch-enemies Iran and Israel.
In April, Iran said another ship, the Saviz, had been targeted in the Red Sea amid reports it had been attacked with limpet mines - mines attached via magnets.
Iran and Israel have blamed one other for a number of attacks on cargo ships since February.
The Kharg was built in Britain and entered service in 1984, and is named after the island that's home to Iran's main oil terminal.
It is one of the few Iranian naval ships that can replenish other vessels and is able to lift heavy cargo and launch helicopters.
The sinking is the latest in a number of recent naval disasters for Iran.
A missile fired during a training exercise in 2020 mistakenly hit a ship - also near the port of Jask, killing 19 sailors; and in 2018 one of its destroyers sank in the Caspian Sea.