Unleashed with joint US and Israeli air strikes on Iran almost two weeks ago, the war has killed about 2000 people and thrown global energy markets and transport into chaos.
The conflict has spread across the Middle East and prompted plans for a record release of strategic oil reserves to dampen one of the worst fuel shocks since the 1970s.
At a rally in Kentucky ahead of November midterm elections in which his Republican party is trailing badly, Trump said the US had won the war but did not want to have to go back every two years.
"We don't want to leave early do we?" he said on Wednesday.
"We got to finish the job."
Oil prices, which shot up this week to nearly $US120 a barrel before retreating, jumped almost 10 per cent back above $US100 a barrel in Asian trade on Thursday amid renewed fears about supply disruption.
Iran has made clear it intends to impose a prolonged economic shock, with an Iranian military spokesman telling the US: "Get ready for oil to be $US200 a barrel because the oil price depends on regional security, which you have destabilised."
Iranian explosive-laden boats appear to have attacked two fuel tankers in Iraqi waters, setting them ablaze and killing one crew member after projectiles struck four merchant vessels in Gulf waters.
The International Energy Agency on Wednesday recommended releasing 400 million barrels from global strategic reserves to dampen one of the worst oil shocks since the 1970s, the biggest such intervention in history.
Trump said the decision "will substantially reduce oil prices as we end this threat to America and the world".
Trump has also authorised the release of 172 million barrels from the US strategic reserve from next week.
Iran also targeted a fuel facility in Bahrain's Muharraq, while drones struck oil storage facilities at Oman's Salalah port.
There has been no sign that ships can safely sail through the Strait of Hormuz, the now-blockaded channel along the Iranian coast that serves as a conduit for around a fifth of the world's oil.
On Wednesday, the Iranian military said the strait was "undoubtedly" under Iran's control, and the G7 agreed to examine the option of providing escort for ships so they could navigate freely in the Gulf.
Trump said US forces had knocked out 58 Iranian naval ships and that Iran was "pretty much at the end of the line".
He said the US would now "look very strongly" at the Strait of Hormuz, adding: "The straits are in great shape. We've knocked out all of their boats. They have some missiles, but not very many."
Trump said earlier ships "should" transit through the strait but sources said Iran had deployed about a dozen mines there, further complicating the blockade.
US and Israeli officials have said their aim is to end Iran's ability to project force beyond its borders and destroy its nuclear program.
Trump and other officials have sent mixed messages about whether regime change was another goal after supreme leader Ayatollah Ali Khamenei was killed in initial strikes and replaced by his son Mojtaba Khamenei, who was lightly wounded.
US intelligence indicates that Iran's leadership is still largely intact and is not at risk of collapse, according to three sources familiar with the matter.
The FBI had reportedly warned of Iranian drones potentially striking the US west coast, although Trump said he was not worried that Iran might attack on US soil.
