Iran and the United States vowed on Thursday to step up attacks, after Tehran's Houthi allies struck Saudi shipping and sent oil prices soaring.

President Donald Trump said the United States would hold Iran responsible for the Houthis' actions and warned both would soon receive a "major military punishment".

The international oil benchmark Brent crude surged past $100 a barrel and European leaders expressed alarm after Yemen's rebels hit oil tankers in the Red Sea.

"The situation is getting out of control. It is teetering on the edge of the unimaginable," United Nations Secretary-General Antonio Guterres warned.

"One crisis feeds another. One escalation triggers the next," he told a meeting of the UN Security Council.