Washington DC - President Donald Trump said Tuesday that no talks with Iran are underway and none are scheduled, after making a fresh jibe at Tehran on social media.

Earlier on Tuesday, Trump posted a map on Truth Social showing the Strait of Hormuz as "NEW U.S. 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 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.

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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. The Naval Blockade remains in full force and effect," Trump wrote on his Truth Social network.

"The Hormuz Strait is open and operating. All water mines have been removed or detonated."

US sources told AFP there had been "positive" discussions with the Iranians, but added that Trump had decided to wait and asked his team not to engage until Iran was ready to make a deal.

In recent weeks, there has been a lull in fighting, though on Tuesday the United Arab Emirates accused Iran of firing two ballistic missiles – which landed at sea – targeting "maritime navigation." Iran, however, denied firing a missile toward the UAE.

Soon after, the UAE announced that "in light of regional escalations" it was halting all trade, commercial exchanges, and financial transactions with Iran.

The UAE bore the brunt of Iranian missile and drone attacks in the first period of the war, but had not reported any attacks since the US and Iran signed a memorandum of understanding in June that was meant to halt the fighting.