The waterway, a major transit point for global energy supplies that Iran has effectively blocked but Trump has vowed to reopen, is crucial to negotiations between the sides during a ceasefire agreed last Tuesday and due to last two weeks.
"We're now starting the process of clearing out the Strait of Hormuz as a favour to Countries all over the World," Trump posted, adding that Iranian mine-dropping vessels had been destroyed.
The US military said two of its warships had passed through the strait and conditions were being set to clear mines, while Iran's state media denied any American ships had transited the waterway.
The talks in Islamabad were the first direct US-Iranian meeting in more than a decade and the highest-level discussions since the 1979 Islamic Revolution.
Trump's Vice President JD Vance, special envoy Steve Witkoff and son-in-law Jared Kushner flew in on Saturday and met Iranian Parliamentary Speaker Mohammad Baqer Qalibaf and Foreign Minister Abbas Araqchi for two hours before a break, according to a source from mediator Pakistan.
The Iranian delegation had arrived on Friday dressed in black in mourning for Supreme Leader Ayatollah Ali Khamenei and others killed in the six-week war.
They carried shoes and bags of some students killed during the US bombing of a school next to a military compound, the Iranian government said.
"There were mood swings from the two sides and the temperature went up and down during the meeting," said another Pakistani source of the first round of talks.
Iran's state-affiliated Nournews said talks would resume later on Saturday night or Sunday.
The war has sent global oil prices soaring, killed thousands of people and seen unprecedented hits on Gulf Arab states.
Amid conflicting versions from officials and media in both nations, the US and Iranian sides appeared to remain far apart.
Before the talks began, a senior Iranian source told Reuters the US had agreed to release frozen assets in Qatar and other foreign banks. But a US official denied that.
As well as release of assets abroad, Tehran is demanding control of the Strait of Hormuz, payment of war reparations and a ceasefire across the region, including in Lebanon, according to Iranian state TV and officials.
Trump's stated goals have varied during the campaign, but as a minimum, he wants free passage for global shipping through the strait and the crippling of Iran's nuclear enrichment program to ensure it cannot produce an atomic bomb.
Mutual distrust is high. "We will negotiate with our finger on the trigger," Iranian government spokesperson Fatemeh Mohajerani said on state TV.
Tehran's agenda includes aiming to collect transit fees in the Strait of Hormuz, a chokepoint for about 20 per cent of global oil and liquefied natural gas shipments.
The biggest ever disruption has fed inflation and slowed the global economy, with an impact expected to last for months even if negotiators succeed in reopening the strait.
Nevertheless, three Liberian and Chinese-flagged supertankers did pass through the strait on Saturday, shipping data showed, marking what appeared to be the first vessels to exit the Gulf since last week's US-Iran ceasefire.
US ally Israel, which joined the February 28 attacks on Iran that launched the war, has also been bombing Tehran-backed Hezbollah militants in Lebanon.
More than 90 people were killed in Israeli air strikes across Lebanon on Saturday, the Lebanese health ministry said, bringing the war's death toll to 2,020 people, including 165 children, nearly 250 women and 85 medics.
Israel and the US have said Lebanon is not part of the Iran-US ceasefire.
