The MV Mercer Street, operated by the London-based company Zodiac Maritime, was off Oman’s coast in the Arabian Sea when the incident occurred on Thursday.
The company, which belongs to Israeli shipping magnate Eyal Ofer, said it was working to establish what had happened.
But Israeli Foreign Minister Yair Lapid on Friday blamed “Iranian terrorism”.
“Iran is not just an Israeli problem,” Mr. Lapid said in a statement, adding: “The world must not be silent.”
However, details of the attack on the Liberian-flagged, Japanese-owned tanker remain unclear. Iran has not yet commented on the allegations.
A spokesperson for the UK government said it was also trying to “urgently establish the facts”.
“Our thoughts are with the loved ones of a British national who has died following an incident on a tanker off the coast of Oman,” the statement said.
In a statement on Friday, Zodiac Maritime announced the two deaths with “profound sadness”. It said no other injuries had been reported.
The company added that the vessel was now “sailing under the control of her crew” and heading to a safe location with a US naval escort.