Brent oil crude soared as much as 4.5% and was trading at $62.07 a barrel at 10:42 a.m.in London.
The mystery incident, the second involving shipping in the strategic sea lane in only a few weeks, came amid spiralling tensions between Tehran and Washington, which has pointed the finger at Iran over tanker attacks in May.
The Bahrain-based U.S. Navy Fifth Fleet said it was assisting the tankers after receiving distress calls following "reported attacks".
The Japan Shipowners' Association said one of the two ships attacked is a Panamanian-registered chemical tanker belonging to its Japanese member and was on its way to Singapore and Thailand, not to Japan.
The Norwegian shipping firm Frontline confirmed that its oil tanker Front Altair was on fire, Norwegian newspaper VG reported earlier in the day, quoting a company spokesman.
The vessel was "on fire and adrift", Dryad added.
The firm that operates the Front Altair told The Associated Press that an explosion was the cause of the fire onboard. The sources suggested the explosions were the result of an attack, though a cause is as yet unconfirmed.More news: Xbox Game Pass for PC: Price, Games, Release Date and More
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CPC said all crew have been rescued from the ships.
The tankers Front Altair and Kokuka Courageous movements are shown in this still image taken from an animation obtained on Thursday from social media.
The tanker association INTERTANKO said two vessels had been attacked in the Middle East and there were growing worries for the safety of ships and their crews sailing through the Strait of Hormuz.
Iran denies claims that it wants to attack USA forces, with its ambassador to the United Nations telling NBC News in May that the rhetoric coming from Washington was risky and mirrored the run-up to the Iraq War.
The timing of Thursday's reported attack was especially sensitive as Abe's high-stakes diplomacy mission was under way in Iran. Japanese foreign ministry says the vessels were carrying "Japan-related" cargo.
On Wednesday, after talks with Iranian President Hassan Rouhani, Abe warned that any "accidental conflict" that could be sparked amid the heightened US-Iran tensions must be avoided. "I don't regard Trump as deserving any exchange of messages", Khamenei reportedly told Abe. His remarks were apparently meant to downplay and lower expectations amid uncertain prospects for Abe's mission.
Tensions in the Middle East have escalated since U.S. President Donald Trump withdrew from a 2015 multinational nuclear pact with Iran and reimposed sanctions, notably targeting Tehran's key oil exports.
Iran's nuclear deal, reached in 2015 by China, Russia, France, Germany, the United Kingdom and the USA, saw Tehran agree to limit its enrichment of uranium in exchange for the lifting of crippling sanctions.