"The Countries of the World that receive Oil through the Hormuz Strait must take care of that passage, and we will help - A LOT!" Trump wrote in a social media post.
"The US will also coordinate with those Countries so that everything goes quickly, smoothly, and well."
Three sources familiar with the efforts told Reuters that Trump's administration had rebuffed efforts by Middle Eastern allies to start diplomatic negotiations aimed at ending the war.
Iran also projected defiance, rejecting the possibility of any ceasefire until US and Israeli airstrikes end.
Iranian forces have kept up their strikes. A drone attack disrupted a major United Arab Emirates energy hub on Saturday, local time, and the US warned its citizens to leave Iraq after a missile attack on the embassy in Baghdad overnight on Friday.
Since Israel and the United States began air attacks on Iran on February 28, the war has killed more than 2000 people, mostly in Iran, according to reports from governments and state media.
At least 15 were killed when an airstrike hit a refrigerator and heater factory in the central Iranian city of Isfahan, the semi-official Fars news agency said on Saturday.
Iran called on civilians in the UAE to evacuate ports, docks and "American hideouts", saying US forces had targeted Iran from those areas.
The UAE denied that the strikes on Iran's Kharg island on Friday night had come via its territory.
Some oil-loading operations were suspended in the UAE's Fujairah emirate, a global ship-refuelling hub, after a drone attack, industry and trade sources said on Saturday.
The emirate's media office said a drone was intercepted, but civil defence forces as of late Saturday were still trying to put out a fire caused by falling debris.
Trump was spending the weekend at his Mar-a-Lago resort in Florida, where he kept a relatively low public profile on Saturday, while posting on his Truth Social account.
In one post, the Republican president wrote that he hoped China, France, Japan, South Korea, Britain and others would send warships to the Strait of Hormuz.
None of those nations gave any immediate indication they would do so. French officials said on Friday their government was pushing on with efforts to assemble a coalition to secure the Strait of Hormuz once the security situation stabilises.
A British Ministry of Defence spokesperson said it was discussing with allies and partners options to ensure the security of shipping in the region.
Iranian Supreme Leader Mojtaba Khamenei, who replaced his slain father, has said the Strait of Hormuz should remain closed.
Separately, Iranian Foreign Minister Abbas Araqchi dismissed speculation from US Defence Secretary Pete Hegseth that Khamenei was wounded and likely disfigured.
"There is no problem with the new supreme leader. He sent his message yesterday, and he will perform his duties," Araqchi told MS Now.
Khamenei has not appeared in public, instead issuing a statement on Thursday read by a television presenter.
Iran played down the extent of the damage on Kharg Island. The US said it had targeted military, not energy industry, targets on the island, which is about 24 kilometres off Iran's coastline in the Gulf.
US Central Command said it hit more than 90 sites on Kharg, including naval mine storage facilities, missile storage bunkers and other military targets.
Araqchi said Iran would respond to any attack on its energy facilities. Iran's Ministry of Defence said on Saturday nine ballistic missiles and 33 drones were launched from Iran towards the UAE.
