Trump has repeatedly insisted that the strait, which Tehran effectively closed at the start of the Middle East war in late February, is under US control despite traffic remaining throttled.

"The Strait of Hormuz has been Iranian, is Iranian, and will remain Iranian," Iranian Deputy Foreign Minister Kazem Gharibabadi said on X.

"This strait will only be closed and opened under Iran's command."

Trump told a political rally in New York state on Friday that after the US defeats Iran, "pretty soon I'll be declaring the Hormuz Strait a territory of the United States".

"It's true," he added.

An unnamed White House official later clarified that Trump was joking, the Wall Street Journal reported.

Last week, a top Iranian official set out a list of conditions for reopening the strait, including an end to the "war and aggression against Iran and its allies in Lebanon, Palestine, Yemen, and Iraq".

Mohammad Bagher Zolghadr also demanded the end of crippling sanctions, the release of frozen assets and compensation for wartime damage.

Ongoing attacks

As diplomacy stalls between the longtime foes, attacks in the Hormuz strait have continued, highlighting the continued risks to regional shipping.

The United Arab Emirates' state-owned oil giant ADNOC said on Saturday that one of its vessels came under attack the night before.

Abu Dhabi's foreign ministry later blamed Tehran, and said that Iran's Revolutionary Guards were engaged in "acts of piracy" in the strait.

On Friday the Gulf nation blamed Iran for other attacks on two vessels linked to ADNOC as they passed through the waterway.

Such attacks led to the collapse of an April ceasefire between the United States and Iran.

As Iran chokes traffic in Hormuz, its Houthi allies in Yemen have also declared a parallel maritime blockade on Saudi ports in the Red Sea, the oil-exporting giant's only other maritime route.

A June deal between Washington and Tehran – meant to serve as a jumping-off point for negotiations on a permanent settlement – had said Iran and Oman would hash out future arrangements for the Hormuz in discussion with other Gulf countries and "in line with the applicable international law".

Before the war, the strait carried around a fifth of the world's oil and LNG exports, and prices have repeatedly surged since the dispute over the waterway erupted, piling economic and political pressure on Washington.

Iran wants to control the strait and charge tolls, powers it did not exercise before the war and ones that the US fiercely opposes.

The closure of Hormuz has driven up prices for US voters, creating a political headache for Trump as November's midterm elections near.

US Vice President JD Vance said this week that Washington's top priority in the Iran war was keeping energy prices low for Americans, while preventing Tehran from acquiring a nuclear weapon ranked second.

Tehran signalled last week that it had agreed with Oman on a route for ships to transit the strait and were finalising arrangements to jointly manage the waterway.

The US has imposed its own retaliatory blockade of Iranian ports in an attempt to cripple its economy.

"We have the blockade. No ships get through unless we want them to," Trump said to a cheering crowd of supporters on Friday.

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