"I want to give them every last chance before decapitation," Trump told reporters on Monday. "You'll find out today or tomorrow. I mean, they're going to go quickly, one way or the other. It's not very complex."

This is a "last chance" for Iran to come to an agreement, the president said, after he called off what he described as a major attack on the Islamic Republic over the weekend that would have likely involved Israel.

A diplomatic resolution appears to hinge on talks between Oman and Iran to get more ships sailing through the strait. There's little sign of progress in those negotiations and Iran continues to take a hard line on the waterway. It insists it has the right to manage maritime traffic and attack vessels that try to sail through the chokepoint without seeking its permission.

Iran's stance underscores the difficultly Trump has faced in wrapping up a war he started in late February and that's sent energy prices soaring, hurting the US leader and his Republic party ahead of midterm elections in November.

Brent crude rose 1.8% on Tuesday to $85.29 a barrel. It's still down about 5% this week after Trump, on Saturday, said he'd hold off on fresh strikes and give diplomacy more time.

The Islamic Republic has vowed to retaliate fiercely against any big US-Israeli strikes. Throughout the conflict, it has shown the ability to cause significant damage to Gulf Arab states such as Kuwait, Bahrain, Saudi Arabia and the United Arab Emirates.

Trump has regularly backed down from threats to launch massive attacks on Iran. If he opts for them this time, that would likely push out oil prices further.

Late Monday, a senior Iranian official called on the US to "take the first step and change its behavior" by returning to the terms of an agreement the two sides reached in June. Mohsen Rezaee, adviser to Iran's supreme leader, told state television that "US warships and bases will be in serious danger" if Trump doesn't lift the blockade of its ports.

Bloomberg reported last week that Muscat and Tehran were discussing reopening the so-called middle passage through Hormuz. It has, however, been mined by Iran, according to people familiar with the matter, and may have to be cleared before vessels use it on a regular basis.