United States President Donald Trump has said no talks with Iran are underway and none are scheduled, as he posted a map showing the Strait of Hormuz as a new US territory.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 US 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 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 US and Israel in late February.Trump revisited the idea again earlier in the week in comments to reporters in the Oval Office.This is not the first time that 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 has even alluded to taking control of the Gaza Strip, without following through on any of these threats.Before the Iran war erupted on 28 February, the Strait of Hormuz was an open waterway with free passage.Iran says it will not reopen the strait until the US meets a sweeping list of demands including ending the US blockade of Iran's ports, lifting oil sanctions, unfreezing Iranian assets and paying war damages."I want to state clearly that the Strait of Hormuz will not be opened until the American commitments stipulated in the memorandum of understanding ..