Emirati officials declined to elaborate on the nature of the sabotage on Sunday, or say who might have been responsible.
One of the two vessels was on its way to pick up crude for delivery to the U.S. when it was hit, according to a statement by Saudi Arabia's Energy Minister Khalid al-Falih, carried by state broadcaster SPA.
The attack did not lead to any casualties or an oil spill but caused significant damage to the structures of the two vessels, he added.
Shortly after the Saudi announcement, Iran's Foreign Ministry called for further clarification about what exactly happened with the Saudi tankers.
The UAE foreign ministry called the attempted sabotage a "dangerous development" and called upon the global community to "prevent such actions" in future. It said the UAE had taken all necessary measures and launched an investigation in coordination with worldwide authorities.
However, the reported incident came after the United States warned ships that "Iran or its proxies" could be targeting maritime traffic in the region, and as America deploys an aircraft carrier strike group and B-52 bombers to the Persian Gulf to counter alleged threats from Tehran, though no official has given details of them.
The U.S. Navy's 5th Fleet, which oversees the region, did not immediately offer comment.
Fujairah's port is located about 140km from the Strait of Hormuz, through which one-third of all oil at sea is traded.
Earlier, the Lebanon-based al-Mayadeen broadcaster said, citing local media, that several large explosions had occurred in the port of Fujairah.
The strait, a vital global oil and gas shipping route, separates the Gulf states and Iran, which has been embroiled in an escalating war of words with the United States over U.S. sanctions and the USA military's regional presence.
The United States announced the deployment of USS Abraham Lincoln and B-52 bombers to the region, with officials telling news outlets that Washington had reports of possible Iranian attacks.
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