Iran's state news agency said it had sunk, although the Norwegian owner had said it was afloat and its crew were safe. International Tanker Management, which operates the vessel, told the Associated Press that its 23 crew had been evacuated by the Hyundai Dubai vessel, which was nearby.
The fleet said it was assisting the two tankers affected, but did not elaborate on any possible cause of the explosions and subsequent fires.
There was no immediate confirmation from ship operators or authorities in Oman or the United Arab Emirates (UAE), in whose territorial waters four tankers were hit last month.
The last reported position for both vessels, as tracked by the website VesselFinder, placed them in close proximity with each other and near the Strait of Hormuz, the narrow choke point separating the Gulf of Oman from the Persian Gulf that Iran has repeatedly threatened to close off in response to US sanctions over Tehran's nuclear weapons program.
Oil prices surged by 4 per cent after the report, which has further stoked tensions following attacks last month on Gulf oil assets amid a dispute between Iran and the U.S. over Tehran's nuclear program. The U.S. claims that Iranian agents used limpet mines to target the ships, none of which sunk despite sustaining damage.
Iran has denied being involved, but it comes as Iranian-backed rebels in Yemen also have launched missile and drone attacks on Saudi Arabia.
Saudi King Salman earlier this month warned a meeting of the Organisation of Islamic Cooperation that "terrorist" attacks in the Gulf region could imperil global oil supplies, as he sought to galvanise support among Islamic countries against arch-rival Iran.
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"Following two attacks on Member vessels this morning, I am extremely anxious about the safety of our crews going through the Strait of Hormuz", Pao lo d'Amico, chairman of INTERTANKO, said in a statement. The vessel, owned by Norway's Frontline, had loaded naphtha, a petrochemical feedstock, from Ruwais in the UAE, according to trade sources and shipping date on Refinitiv Eikon.
Iran said its navy had rescued 44 crew members after the two vessels caught fire in "accidents" off its coast.
The Japan Shipowners' Association said one of the two ships attacked is a Panamanian-registered chemical tanker belonging to its Japanese member and was on its way to Singapore and Thailand, not to Japan.
"All crew safely abandoned the vessel and was picked up by Vessel Coastal Ace".
Hamburg, Germany-based BSM said the Kokuka Courageous "remains in the area and is not in danger of sinking" and that the cargo was "intact".
Thursday's incident came as Japanese Prime Minister Shinzo Abe was wrapping up a two-day trip to Iran with a mission to ease tensions between Tehran and Washington.
"Iran is concerned by the suspicious events around commercial tankers related to Japan", Foreign Ministry spokesman Abbas Mousavi, was quoted as saying on Fars news agency.
The attacks the United States blamed on Iran in May occurred off the Emirati port of Fujairah, also on the Gulf of Oman, approaching the critical Strait of Hormuz, the narrow mouth of the Persian Gulf through which a third of all oil traded by sea passes.