Iran's IRNA reported that Iranian search and rescue teams picked up 44 sailors from the two damaged tankers and took them to the Iranian port of Jask.
It was not immediately clear who was responsible for Thursday's attacks, but the US blamed Iran for last month's bombing of four tankers in the same general area, without offering a clear explanation as to why.
Iranian Foreign Minister Mohammad Javad Zarif described the tanker explosions as "suspicious" https://www.reuters.com/article/mideast-tanker-iran-zarif/irans-zarif-calls-oil-tanker-incidents-suspicious-wants-regional-talks-idUSD5N20801L on Twitter and called for regional dialogue.
In May, the US rushed an aircraft carrier strike group and other military assets to the Persian Gulf region in response to what it said were threats from Iran.
Trump warns on May 19 that if Iran attacks American interests "that will be the official end of Iran". "The US Government is providing assistance and will continue to assess the situation".
The ship's owner, Frontline, said the Marshall Islands-flagged vessel was on fire but denied reports on Iran media it had sunk.
The Gulf of Oman lies at one end of the strategic Strait of Hormuz, and this incident will further increase tension in a vital shipping lane through which hundreds of millions of dollars of oil pass.
The U.S. Navy's Bahrain-based 5th Fleet did not immediately respond to a request for comment. He said they were handed to a U.S. Navy vessel.
Iran's nuclear deal, reached in 2015 by China, Russia, France, Germany, the United Kingdom and the USA, saw Tehran agree to limit its enrichment of uranium in exchange for the lifting of crippling sanctions.
"You should know that if we planned to produce nuclear weapons, America could not do anything", said Khamenei, who has final say on all matters of state in Iran's Shiite theocracy.
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"The shipping industry views this as an escalation of the situation, and we are just about as close to a conflict without there being an actual armed conflict, so the tensions are very high", said Jakob P. Larsen, head of maritime security for BIMCO, the largest worldwide association representing ship owners.
In a printed statement describing the conclusions, the UAE, Saudi Arabia and Norway said the attacks required trained divers, explosive charges placed under the waterline, near the engines, so as to not sink the ships or detonate their cargoes, which indicated a knowledge of the design of the targeted ships.
The first shot hit the tanker above the sea level and the ship caught fire briefly before it was extinguished, he said. Staff on the Kokuka Courageous were evacuated to US Navy ship the Bainbridge.
The Front Altair came from Ruwais in the UAE, a loading point for the state-run Abu Dhabi National Oil Co., according to the data firm Refinitiv.
The fact that both vessels remained afloat suggested mines may have damaged them, said Jakob P. Larsen, head of maritime security for BIMCO, the largest global association representing ship owners.
Tensions between Iran and the United States have been growing since President Donald Trump past year withdrew from an global agreement aimed at restricting Iran's nuclear programme and reinstated economic sanctions that have had a devastating effect on the Iranian economy.
The timing of Thursday's reported attack was especially sensitive as Abe's high-stakes diplomacy mission was underway in Iran. He delivered a note from Trump to Khamenei, but the Ayatollah rebuffed the overture and said he could not expect honest negotiation from the USA administration.
Meanwhile, in Tokyo, Japan's Chief Cabinet Secretary Yoshihide Suga, a top government spokesman, told reporters that Abe's trip was meant to help de-escalate Mideast tensions - not specifically mediate between Tehran and Washington.
His message came just hours after Yemen's Iranian-backed Houthi rebels attacked a Saudi airport, striking its arrivals hall before dawn and wounding 26 people Wednesday.
On June 13, Ayatollah Khamenei reiterated that he rejected Trump's offer to discuss a new agreement, stating, "I do not consider Trump as a person worth exchanging any message with".