A Norwegian company that owns one of the ships, the Front Altair, confirmed that it was on fire. The crews of both vessels — about 23 in one and 21 in the other — were evacuated in lifeboats.
The owners and operators of both vessels described the incidents as deliberate attacks.
A senior American official said intelligence analysts were poring over imagery as well as signals intercepts to help determine what happened and who was responsible.
A Navy P-8 surveillance plane flying over the stricken tankers spotted an unexploded limpet mine attached to the hull of one of the damaged ships, the Panama-flagged Kokuka Courageous, a Defense Department official said, and crew members had also noticed the same type of mine after an initial explosion aboard prompted their evacuation. The similarity to the mine used in the attacks last month bolstered speculation that Iran may have been behind both episodes.
One of the crippled ships, the Front Altair, is owned by the Norwegian shipping company, Frontline, and is registered in the Marshall Islands. CPC Corporation, the Taiwanese oil company, had chartered it to carry naphtha, a petroleum product, from the Emirati port of Ruwais to Kaohsiung, Taiwan.
The Kokuka Courageous was carrying methanol, headed from the Saudi port of Al Jubail to Singapore. Yutaka Katada, the president of the ship’s operator, Kokuka Sangyo, told a news conference that its Filipino crew had abandoned ship in lifeboats after what he described as two attacks three hours apart.
The tanker’s owner, Bernhard Shulte, said in a statement that it had sustained damage on the right side and that one crew member had been slightly injured, but that the ship was not in danger of sinking and its cargo was “intact.”
Shipping industry representatives underscored the channel’s critical importance. “We have people of every nationality and vessels of every flag transiting that crucial sea lane every day,” Paolo d’Amico, the chairman of the International Association of Independent Tanker Owners, said in a statement. “Some 30 percent of the world’s crude oil passes through the Straits. If the waters are becoming unsafe, the supply to the entire Western world could be at risk.”
Analysts in the Arab Persian Gulf states argued that Iran was testing the will of Mr. Trump. “What is Trump going to do? is the key question now,” said Abdulkhaleq Abdulla, an prominent Emirati political scientist. “American credibility is at stake.”