Iran said its navy rescued several dozen crew members of the two vessels, while the US Navy said it had picked up 21 from the Kokuka Courageous.
The Japanese ship operator of the Kokuka Courageous, one of the vessels attacked, said sailors on board the tanker saw "flying objects" just before the attack, suggesting the vessel wasn't damaged by mines.
Other Iranian small boats have remained near the stricken oil tanker since the attack early Thursday, the official added.
Iran has rejected the USA accusation against it as "baseless".
Foreign Minister Mohammad Javad Zarif tweeted on Friday that the United States administration had "immediately jumped to make allegations against Iran without a shred of factual or circumstantial evidence".
Tensions between the United States and Iran are high after the USA pulled out from the Iran nuclear deal and reimposed sanctions preventing Iran from accessing the U.S. financial system and trading in the dollar.More news: Chinese boat fled after sinking Filipino crew, Manila says
A US official told Fox News an Iranian gunboat approached the Kokuka Courageous later in the day and removed the unexploded triangular-shaped limpet mine, the same type of mine used to damage four other tankers in the Gulf of Oman last month. "However, we will defend our interests".
Reuters came out with the story quoting the U.S. military that doesn't prefer opening up new conflict in the Middle East but might not refrain from securing the national interest. "However, we will defend our interests", Centcom concluded.
Kuwait's Ambassador Mansour al-Otaibi said council members condemned the violence and that many of them called for an investigation to determine the facts.
"We are taking this extremely seriously and my message to Iran is that if they have been involved, it is a deeply unwise escalation which poses a real danger to the prospects of peace and stability in the region".
The Norwegian Maritime Authority said three explosions were reported on the Norwegian-owned tanker Front Altair after it was "attacked", leading to a fire and fears at one point the ship would sink.
But much of the chronology centred on the movement of nearby Iranian ships, and what Central Command said was an Iranian order to take control of Altair sailors who had been rescued. Joshua Frey, a 5th Fleet spokesman. Japanese public broadcaster NHK, citing Kokuka Sangyo's chief executive officer, said the ship was hit by a shell.
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Magnetic limpet mines were previously used by Iran to sabotage oil tankers during the so-called "Tanker War" in the late 1980s.
Pompeo told journalists on Thursday that the U.S. assessment of Iran's involvement was based in part on intelligence, as well as the expertise needed for the operation.
On May 12, four oil tankers - two Saudi, one Norwegian and one Emirati - were damaged in still unexplained attacks in the Gulf of Oman off the United Arab Emirates. It is thought implausible that an IRGC group has gone rogue, or even that Houthi rebels fighting Saudi Arabia in neighbouring Yemen were responsible.
"Taken as a whole, these unprovoked attacks present a clear threat to global peace and security, a blatant assault on the freedom of navigation and an unacceptable campaign of escalating tension by Iran", he said.
Pompeo said there was strong evidence of Iran's culpability "based on the intelligence, the weapons used, the level expertise needed to execute the operation" and only Iran in the region had the ability to undertake such an operation.
As the first Japanese prime minister to visit Iran in 41 years, Abe was hoping to serve as a mediator between Tehran and Washington, with tensions having flared in recent weeks and concern growing about possible inadvertent military clashes in the region.More news: Boris Johnson launches bid to become UK Prime Minister