US President Donald Trump said Tuesday that no talks with Iran are under way or scheduled, as he posted a map showing the Strait of Hormuz as a new American territory in a fresh jibe at Tehran.

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Trump has been pressing his threat to claim sovereignty over the crucial energy waterway as the nearly six-month-old Iran war grinds on with little sign of resolution. Trump's envoy and son-in-law Jared Kushner had said on Monday that the United States and Iran were having "very positive and active conversations," but the president denied that was the case.

"There are no talks or conversations going on, or scheduled, with the Islamic Republic of Iran. The Naval Blockade remains in full force and effect," Trump wrote on his Truth Social platform. "The Hormuz Strait is open and operating. All water mines have been removed or detonated."

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Earlier Tuesday, Trump posted a map on Truth Social showing the Strait of Hormuz as "NEW US Territory." Iran has effectively shut down the chokepoint, through which a fifth of the world's oil would usually transit, in retaliation for the war launched by the United States and Israel in late February.

Trump first raised the idea of a US takeover last Friday, saying in a jovial tone he would soon declare it US territory, prompting Iran to retort that the strait "will remain Iranian." He revisited the idea again Monday in comments to reporters in the Oval Office.

Top Iranian negotiator Mohammad Baqer Qalibaf said in comments published by state media that the strait would remain shut until the US met the conditions of the interim deal signed with Iran in June, including lifting the blockade of Iranian ports, lifting oil sanctions, releasing Tehran's frozen assets, and ending military operations on all fronts. Qatar, a key mediator in stalled peace talks, said it is working on an agreement between Iran and Oman over managing the strait as a step toward resuming negotiations to end the conflict.

This is not the first time Trump, faced with a foreign policy obstacle, has threatened to annex foreign territory. Since returning to power in 2025, he has threatened to make Canada the 51st US state, seize Greenland and Cuba, and alluded to taking control of the Gaza Strip, without following through on any of these threats.