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The official Saudi news agency SPA said the attack had been carried out by Yemeni Houthi militants.
The tanker is carrying about 2 million barrels of crude to Ain Sukhna in Egypt, the main offloading point for the SUMED pipeline into the Mediterranean.
The strike was launched on Tuesday when the tanker was near the Yemeni port of Hodeidah, in international waters near the Bab al-Mandab strait, according to a spokesman for the Saudi-led coalition fighting in Yemen.
The EU Naval Force operating around the southern Red Sea, the Gulf of Aden and a large part of the Indian ocean is investigating the incident and said it is likely to be related to the conflict in Yemen.