WASHINGTON — The U.S. is touting progress toward a peace deal with Iran to end the nearly three-month war, even amid fresh hostilities and uncertainty over the vital Strait of Hormuz.

Security in the crucial energy waterway remained unclear Tuesday after the two sides exchanged strikes overnight and U.S. Central Command pushed back on reports that suggested the military was helping escort vessels.

The renewed clashes occurred just hours after U.S. President Donald Trump said negotiations with Tehran to extend their ceasefire and reopen the strait are proceeding. Secretary of State Marco Rubio has cautioned that any deal would likely take a few days to finalize.

Global benchmark Brent rose to trade around $100 a barrel after slumping more than 7% on Monday. Stocks rose toward a record as hopes for a peace deal overshadowed the military action.

One contentious issue under discussion is Iran’s $24 billion in frozen assets, with Tehran wanting half that amount released upon the signing of an agreement, the semi-official Tasnim news agency reported. That element is particularly controversial among Iran hawks in the U.S., who are concerned about conceding too much to the Islamic Republic.

The U.S. military said it conducted self-defense strikes in southern Iran on Monday night, targeting missile-launch sites and boats attempting to lay mines, while the Islamic Revolutionary Guard Corps said it fired at an F-35 fighter jet and several drones after they entered Iranian airspace.

Iran’s Foreign Ministry condemned the U.S. attacks as a violation of a ceasefire that’s been in place since early April, while Supreme Leader Mojtaba Khamenei published a statement warning that the “nations and lands of the region will no longer be a shield for American bases.”

Rubio said Trump would either agree to a good deal or make no agreement at all. The president is under pressure from the likes of Republican Senator Lindsey Graham, who wants a blockade of Iranian ports to remain in place and more strikes to further weaken the Iranian military.

Trump has to balance those pressures with the increasing unpopularity among Americans of the war, which began with a U.S.-Israeli bombardment of Iran in late February. The conflict and Iran’s effective closure of Hormuz have caused energy prices, including gasoline, to soar and are pushing up inflation globally.

Arab states including Saudi Arabia, the United Arab Emirates and Qatar have urged Trump to continue with diplomacy. They fear a return to hostilities would cause Iran to fire drones and missiles on their countries, as it did before the April truce, causing tens of billions of dollars of damage and killing scores of people.

On Monday, Trump in a social media post urged Saudi Arabia, Qatar and other countries to join the Abraham Accords and recognize Israel. That appears unlikely unless Israel takes steps toward allowing a Palestinian state, which its government has ruled out.

Beyond the frozen funds, obstacles to a U.S.-Iran pact include Tehran’s reluctance to allow ships free passage through the Strait of Hormuz. The U.S., Arab states and Europe say it must, but Iranian officials say they want to charge fees for navigation services.

Trump also wants Iran to commit to handing over or destroying its stocks of highly-enriched uranium, which the U.S. fears could be used to build an atomic bomb. Iran has publicly rejected that, though it’s also signaled it may send the stocks to a third country, with Russia and China being the most likely candidates.

Lebanon, where Israel is fighting Iran-backed Hezbollah militants, is another sticking point. Iran insists on a ceasefire there too, while Israel has said it must be allowed freedom of action.

“Even if the two sides are able to reach a deal — and that’s already a big ‘if’ — there is little hope they can then reach a stable peace,” said Dina Esfandiary, an analyst at Bloomberg Economics.

Here’s more on the Iran war:

•A little-known Swiss trading company played a key role in the Hormuz transit of an oil supertanker whose stop-start journey captivated the energy market earlier this month, according to people familiar with the matter.

•Abu Dhabi National Oil Co. has been quietly ferrying oil and gas shipments out of the Persian Gulf using its own fleet, apparently clearing both the Iranian navy and U.S. warships to reach energy-starved customers.

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—With assistance from John Bowker, Vivien Ngo and Tony Capaccio.

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