Iran maintains it effectively controls much of the waterway and intends to impose a toll system in response to the US war launched by Trump on 28 February.
President Donald Trump said on Wednesday that the United States is in control of the strategic Strait of Hormuz and will "keep it."
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"The U.S.A. has total control over the Strait of Hormuz. I THINK WE WILL KEEP IT!" Trump wrote in a post on his Truth Social platform.
"Our Naval Blockade is being called, by everyone, 'A WALL OF STEEL,' and there is nothing Iran can do about it."
Trump has repeatedly claimed the United States controls the strait, which is vital for the flow of energy and other commodity shipping through the Middle East.
However, Iran says it effectively controls much of the waterway and intends to impose a toll system in response to the US war launched by Trump on 28 February.
Late on Tuesday, Trump told reporters: "We have total control over the Hormuz Strait right now. They don't have control. We have total control. We own it."
US and Israeli forces have heavily bombed Iran's military and killed a swathe of the country's leadership so far in the nearly six month war, launched initially with goals including forcing Tehran to abandon its nuclear power programme and regime change.
Iran has resisted with missile attacks on US bases in the region, Israel and targets in US-allied Gulf countries.
Its most effective response has been to strike shipping in Hormuz, effectively snarling the trade route, rattling the world economy.
With his political popularity sinking at home ahead of the November midterm congressional elections, Trump has backed off threats to escalate the war in search of a decisive victory.
That leaves the war in a standoff.
However, the Republican says that the United States is prepared to focus on blockading Iranian ports in a strategy that he told Axios was "low-keying."
"We are only semi-negotiating with them. We are just watching Iran with its huge inflation and the fact they have no money," Trump told Axios on Sunday.