Several US cabinet officials,including Secretary of State Mike Pompeo and US Secretary of Energy Rick Perry,have blamed Tehran for the attacks,which cut 5 per cent of world crude oil production.
Iran has denied responsibility,with Iranian President Hassan Rouhani saying the strike was carried out by"Yemeni people"retaliating against attacks by the Saudi-led coalition in Yemen's four-year-old war.
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Trump said on Monday the US had a lot of options to respond to the attacks,but declined to say what measures he was considering. He added that,while the US could help,he had not promised protection to Riyadh.
"With all that being said,we'd certainly like to avoid it,"Trump said about a war with Iran,adding that he has not yet concluded that diplomacy has run its course.
"I don't want war with anybody,"he says.
The attacks on Saudi Arabia have damaged the globe's largest crude processing plant and triggered the biggest jump in oil prices in nearly 30 years.