The Bahrain-based U.S. Navy Fifth Fleet said it was assisting the tankers after receiving distress calls. The United Kingdom Maritime Trade Operations, part of Britain's Royal Navy, said it was investigating with its partners.
Full details about Thursday's incident were not immediately clear. The firm which chartered one of the vessels said it suspected a torpedo had hit the ship, while a source said the other might have been damaged by a magnetic mine.
An investigation blamed limpet mines for last month's attacks on four tankers. Saudi Arabia and the United States blamed Iran for those attacks, a charge Tehran denies.
Oil prices LCOc1 surged as much as 4% after Thursday's news. The region was already on edge following attacks in May on Gulf oil assets that occurred amid a dispute between Iran and the United States over Tehran's nuclear programme.
The Gulf of Oman lies at the entrance to the Strait of Hormuz, a major strategic waterway through which a fifth of global oil consumption passes from Middle East producers.
There was no immediate confirmation of Thursday's incident from authorities in Oman or the United Arab Emirates, in whose territorial waters the four tankers were hit in May.
Saudi Arabia and the UAE have said attacks on oil assets in the Gulf pose a risk to global oil supplies and regional security.
Bernhard Schulte Shipmanagement said its tanker Kokuka Courageous was damaged in a "suspected attack" that breached the hull above the water line while transporting methanol from Saudi Arabia to Singapore.
"The ship is safely afloat," it said in a statement, adding that its crew were safe with one minor injury reported.
A shipping broker said there had been an explosion "suspected from an outside attack" that may have involved a magnetic mine on the Kokuka Courageous. "Kokuka Courageous is adrift without any crew on board,” the source said.
Japanese shipping firm Kokuka Sangyo, owner of the Kokuka Courageous, said its ship had been hit twice over a three-hour period.
Taiwan's state oil refiner CPC said tanker Front Altair, owned by Norway's Frontline, was "suspected of being hit by a torpedo" around 0400GMT, as it carried 75,000 tonnes of the petrochemical feedstock naphtha to Taiwan. It said the crew were safe.
Frontline said its vessel was on fire, but still afloat, although the Iranian news agency IRNA later said the vessel had sunk. However, there was no immediate independent confirmation.
The Front Altair loaded its cargo from Ruwais in the UAE, according to trade sources and shipping data on Refinitiv Eikon.
Another source said the Front Altair reported a fire caused by a "surface attack" and that the crew had been picked up by nearby vessel Hyundai Dubai.
Iran's state news agency IRNA reported that Iranian search and rescue teams had picked up 44 sailors from two damaged tankers and had taken them to the Iranian port of Jask.
Thursday's suspected attacks came a day after Yemen's Iran-aligned Houthis fired a missile on an airport in Saudi Arabia, injuring 26 people. The Houthis also claimed an armed drone strike last month on Saudi oil pumping stations.
Japanese Prime Minister Shinzo Abe, speaking during a visit to Iran on Wednesday, urged all sides not to let tensions escalate. He met Iran's Supreme Leader Ali Khamenei on Thursday.
(Reporting by Koustav Samanta and Jessica Jaganathan in Singapore, Liang-Sa Loh and Yimou Lee in Taipei, Terje Solsvik in Oslo and Jonathan Saul in London; Editing by Richard Pullin and Edmund Blair and Jon Boyle) ((Jessica.Jaganathan@thomsonreuters.com; +65 6870 3822; Reuters Messaging: firstname.lastname@example.org; Twitter: https://twitter.com/j3ssi3))