Oil prices surged after Trump said military operations would be intensified in the next two to three weeks, offering no concrete timeline for ending a conflict that sparked global energy supply chaos and has threatened to send the world economy into a tailspin.
"I can say tonight that we are on track to complete all of America's military objectives shortly, very shortly," Trump said in a Wednesday evening prime-time speech.
"We're going to hit them extremely hard over the next two to three weeks. We're going to bring them back to the Stone Ages where they belong."
Trump also suggested the war could escalate if Iranian leaders did not give in to US terms during negotiations, with strikes on Iran's energy and oil infrastructure possible.
Benchmark Brent crude prices jumped about five per cent to $US106.16 per barrel, with little reassurance from Trump's address about how the critical Strait of Hormuz energy conduit would reopen.
Prices had fallen earlier on Thursday after settling lower in the previous session.
Shortly after Trump's speech, the Israeli military said it had identified missiles launched from Iran towards Israeli territory.
Thousands of people have been killed across the Middle East since February 28, when the US and Israel struck Iran, triggering Iranian attacks on Israel, US bases and the Gulf states, while opening a new front in Lebanon.
Iran also all but closed the Strait of Hormuz, a vital waterway carrying about a fifth of global oil and liquefied natural gas, pushing up energy costs and weighing on Trump's sagging approval ratings months before pivotal midterm congressional elections.
But Trump in his speech said the US did not need the strait and he challenged allies who relied on oil in the region to work towards reopening it.
"Many Americans have been concerned to see the recent rise in gasoline prices here at home," Trump said.
"This short-term increase has been entirely the result of the Iranian regime launching deranged terror attacks against commercial oil tankers of neighbouring countries that have nothing to do with the conflict."
In an interview with Reuters, Trump said US-Israeli strikes had ensured Iran would not obtain nuclear weapons, adding that US forces could return with "spot hits" if the threat resurfaced.
"They were right at the doorstep (of a nuclear weapon)," Trump said in his TV address, without providing evidence, touting what he said were "swift, decisive, overwhelming victories on the battlefield".
"We are systematically dismantling the regime's ability to threaten America or project power outside of their borders."
Before Trump's remarks, Iranian President Masoud Pezeshkian said in a letter addressed to the American people that his country harboured no enmity towards ordinary Americans.
Trump said discussions were ongoing with Iranian leaders he considered less radical than previous leaders.
On social media on Wednesday, he said Iran had requested a ceasefire but that would not be considered until its Strait of Hormuz blockade ended.
Iran denied making any such request.
Trump had suggested on Tuesday he could wind down the war soon without a deal, and scaled up threats to withdraw from NATO over what he considered its lack of support for US objectives in Iran.
In his address, Trump urged countries in need of oil to buy it from the US or to "go to the strait and just take it".
"Iran has been essentially decimated. The hard part is done, so it should be easy."
European states have sought to appear unruffled, and France's junior army minister Alice Rufo said operations by NATO in the Strait of Hormuz would be a breach of international law.
