A memorandum of understanding the US and Iran signed in June that gave them a 60-day window to negotiate a lasting peace deal technically expired Monday, and when Trump was asked if he would seek an extension, he replied: "No." The ceasefire had been repeatedly violated in any event, with intermittent clashes continuing, and both sides had declared it defunct.

Brent crude climbed as much as 1.1% to $91.85 a barrel on Tuesday — its highest level in more than three weeks — as prospects dimmed for a swift reopening of Hormuz, through which a fifth of the world's oil and gas transited before the war. Trump is demanding that free passage through the waterway be restored, while Iran said it will govern traffic in conjunction with Oman.

Several ships have been attacked along the route linking the Persian Gulf to the Gulf of Oman and the Arabian Sea in recent days and traffic is a fraction of what it was prior to the war. On Tuesday, the UK Navy said a vessel heading out of the strait was struck by a projectile that damaged its engine room, resulting in one casualty.

The war erupted on Feb. 28, when the US and Israel launched airstrikes against Iran and sparked parallel conflicts that have embroiled much of the Middle East. Trump has repeatedly said his primary objective is to prevent the Islamic Republic from obtaining a nuclear weapon, an objective it has denied pursuing.

Trump on Monday said the US retains leverage over Iran, citing the naval blockade of its ports. He reiterated his idea of declaring Hormuz an American territory, insisting the US had total control — remarks directly at odds with those of Iranian officials.

Iran and Oman are negotiating a deal on how Hormuz should be managed, but the US isn't part of those discussions. In a phone interview with Fox News, Trump warned that if "Oman gets in the way we'll bomb the s—— out of them," without giving any further details, repeating a similar threat he made in May. Oman isn't a formal US military ally, but has served as a close security partner.