Trump previously said the US had completely destroyed 10 inactive mine-laying vessels.
In apparent response to media reports that Iran had begun laying mines in the waterway, a key passage for oil shipments, Trump posted on Truth Social: "If Iran has put out any mines in the Hormuz Strait, and we have no reports of them doing so, we want them removed, IMMEDIATELY!"
He said that if Tehran did not do so it would face military consequences, without providing details.
Trump also said the US was using the same technology deployed against drug traffickers to "permanently eliminate any boat or ship attempting to mine the Hormuz Strait".
In recent months, the US has carried out a series of strikes on vessels in the Caribbean and eastern Pacific that it alleges were carrying drugs, killing dozens of people.
The Pentagon said earlier on Tuesday it was striking Iranian mine-laying vessels and mine storage facilities.
The US-Israel war against Iran has already effectively halted shipments through the Strait of Hormuz, along Iran's coast, where a fifth of global oil and liquefied natural gas normally passes.
The top US general said earlier on Tuesday, local time, the military has started looking at ways to potentially escort ships through the Strait of Hormuz, should it be ordered to do so.
"We're looking at a range of options there," General Dan Caine told reporters at the Pentagon.
However, the US navy has so far refused near-daily requests from the shipping industry for military escorts through the Strait, sources familiar with the matter told Reuters.
Secretary of Energy Chris Wright posted on social media platform X on Tuesday that the navy had successfully escorted an oil tanker through the waterway, but later deleted the post.
The United States has not yet escorted any oil tankers or vessels through the Strait of Hormuz, White House Press Secretary Karoline Leavitt told reporters when asked about the issue at a press conference later on Tuesday.
"A video clip was deleted from Secretary Wright's official X account after it was determined to be incorrectly captioned by Department of Energy staff," a department spokesperson said.
Commenting on Wright's remarks, a spokesperson for Iran's Revolutionary Guards denied an oil ship had been escorted.
"Any movement of the US fleet and its allies will be stopped by our missiles and drones," Ali Mohammad Naini said in comments carried by Iranian state media.
