US officials say all 21 sailors from the Kokuka Courageous, the other tanker that was hit, have been treated and returned to their ship and are preparing to tow the strick vessel back to port after they were rescued by the American guided-missile destroyer Bainbridge.
The president insisted that the Strait of Hormuz, a key commercial shipping route, would not be closed in the wake of the attacks on the two tankers in the Gulf of Oman.
Asked how to he planned to address Tehran and stop any further similar incidents, Trump said: "We're going to see".
Tensions continue to rise over the alleged attack by Iran on two oil tankers in the Gulf of Oman as the United States military released video footage that it claims shows an Iranian military patrol boat approach one of the vessels.
Trump spoke with Abe on Friday, discussing issues including Abe's "recent travel to Iran and the circumstances surrounding the attacks on two tankers in the Gulf of Oman", according to a White House statement.
The operator of the Kokuka Courageous, BSM Ship Management, said its crew abandoned ship and were rescued by a passing vessel.
The Norwegian-MT Front Altair was set ablaze and burned for hours, a spectacle caught on camera and broadcast by Iranian state-owned news service Press TV.
Gheit told reporters that he did not believe an Arab country was "trying to obstruct naval lanes or to shoot itself in the foot by acting the way we have seen in the Gulf of Oman or in the Hormuz Strait".
He said the US made the judgement "based on intelligence, the weapons used, the level of expertise needed to execute the operation, [and] recent similar Iranian attacks on shipping".
Iran has rejected accusations by U.S. secretary of state Mike Pompeo that it was responsible.
Tensions have spiked further since Trump acted last month to force Iran's oil customers to slash their imports to zero or face draconian USA financial sanctions.More news: Halo Infinite Confirmed To Be An Xbox Scarlett Launch Title
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No other state or non-state actor could plausibly have been responsible.
"Iran has a history of doing this", he said.
A statement late Thursday from the mission also called on the worldwide community to prevent "the reckless and risky policies and practices of the USA and its regional allies in heightening the tensions in the region".
It was also based on recent incidents in the region, which the USA also blamed on Iran, including the use of limpet mines in the Fujairah attack, he said.
Iranian Foreign Minister Mohammad Javad Zarif said the two oil tanker incidents were "suspicious" and called for regional dialogue to avoid tensions. The US at the time blamed Iran - but Tehran denied the accusations.
"These latest attacks build on a pattern of destabilising Iranian behaviour and pose a serious danger to the region", he said.
In Washington, Secretary of State Mike Pompeo blamed Tehran, citing the type of explosives used and what he said was the sophistication of the attacks.
Explosions also struck the Japanese-owned Kokuka Courageous, which was loaded with methanol, but the fire on board was soon extinguished.
"It's not a great video and you cant see much detail it could but it looks like what the U.S. says it is", said Richard Meade, the editor of Lloyd's List, a shipping intelligence agency.
The tensions between the United States and Iran are already high over the U.S. pullout from the 2015 nuclear accord and the reimposition of economic sanctions.
Iranian Foreign Minister Mohammad Javad Zarif rejected the US accusations as part of "sabotage diplomacy".