The Mercer Street was attacked off the coast of Oman, and two on board were killed
The UK and US believe Iran was behind a tanker attack that killed two people, and have vowed to respond, calling it a violation of international law.
The MV Mercer Street, operated by an Israeli-owned firm, was attacked off Oman on Thursday.
A British national and a Romanian citizen were killed.
The statements came after Israel's Prime Minister Naftali Bennett said there was "evidence" that its longstanding foe Iran was responsible.
Mr Bennett warned that "we know how to send a message to Iran in our own way", while Tehran rejected what it called the "baseless accusations".
The attack on the MV Mercer Street appears to be the latest escalation in an undeclared "shadow war" between Israel and Iran.
For months there have been several attacks on both Israeli and Iranian-operated vessels, which are seen as tit-for-tat incidents, though casualties are rare.
Iran has also accused Israel of targeting its nuclear sites and scientists.
In a statement on Sunday, UK Foreign Secretary Dominic Raab said London believed Iran had used one or more drones against the MV Mercer Street, calling it "deliberate, targeted, and a clear violation of international law".
"Iran must end such attacks, and vessels must be allowed to navigate freely," he added.
US Secretary of State Antony Blinken said Washington was also "confident that Iran conducted this", and that an "appropriate response" would follow.
Israel's Prime Minister said it expected the international community to make clear to Iran that it had made a serious mistake.
Iran conceded nothing in response. Its foreign ministry spokesman, Saeed Khatibzadeh, told reporters that "the Zionist regime (Israel) has created insecurity, terror and violence".
He said Israel "must stop such baseless accusations", warning: "Whoever sows the wind reaps the whirlwind."
The escalation comes against the backdrop of thorny talks between Iran and world powers in Vienna to try to revive a frayed 2015 deal curbing Iran's nuclear programme.
Western countries suspect Iran might be seeking to build nuclear weapons in violation of conventions - something Iran strongly denies.
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