It said the blasts were "probably caused by missile strikes".
The National Iran Oil Company said a supertanker called Sinopa was hit by two missiles around 60 miles from the port of Jeddah, leaving it badly damaged.
The incident comes amid heightened tension between Iran and Saudi Arabia.
"All the ship´s crew are safe and the ship is stable too", said NITC, adding those on board were trying to fix the damage.
All reports said the reported explosion happened off the coast of Jeddah on the Red Sea.
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The blast caused heavy damages to the tanker, according to the semiofficial ISNA news agency.
"Experts believe it was a terrorist attack", the news report said.
All crew members of an Iranian oil vessel that was on fire in the Red Sea after an explosion are safe and the situation of the tanker is stable, Iran's Nour news agency reported on Friday. The U.S. Navy's 5th Fleet, which oversees the Mideast, says it was aware of the incident, but declined to immediately comment further.
Yemens Houthi group claimed responsibility for the attacks, but a USA official said they originated from southwestern Iran.
The incident comes amid growing tensions between Iran and the USA and its allies in the Persian Gulf following a series of suspected sabotage attacks off the coast of the United Arab Emirates in mid-May.
Relations between Washington and Tehran have steadily deteriorated since last year's nuclear-deal withdrawal by the United States.