"The Hormuz Strait is OPEN, and will remain OPEN, with or without Iran. We are reinstating THE IRANIAN BLOCKADE," Trump said on Truth Social.
"The USA ... will be reimbursed, at the rate of 20 per cent on all cargo shipped, for any and all costs necessary to do the job of providing safety and security to this very volatile section of the World," he said.
He said the process would begin immediately but did not elaborate.
The US president floated the idea earlier in a phone interview on Fox News, saying the US would probably take over the strait and should be reimbursed.
"We're going to keep the strait, and we'll probably run it. We'll become the guardian of the strait. Maybe we'll call it the guardian angel of the strait. And we should be reimbursed for that," he told the broadcaster.
Control of the Strait of Hormuz, a vital route for global oil supplies, has become one of the main battlegrounds of the conflict.
Iran's effective blockade of the strait has pushed up energy prices and increased concerns about inflation globally.
"We're going to be reimbursed, because the other nations are very wealthy. They're on our side, and we can't be expected to do that for nothing," he said.
After announcing the waterway's closure on Saturday following what it described as an unauthorised transit, Iran said on Sunday that passage remained suspended and that permits would be issued once "stability and calm" were restored.
"We had a deal. It was a done deal, and then they broke it. They always break it. We've had 10 deals with these people, and so we're just going to hit them very hard," Trump said.
Iran's Revolutionary Guards said in a statement on Monday that the only way to restore regular shipping traffic through the strait was to end US military interventions in the waterway, and warned that "continued interference could lead to greater incidents in the global oil and gas sector".
US and Iranian forces exchanged heavy missile and drone attacks over the weekend and into Monday, with Iran saying it had struck US military facilities across the Gulf and kept the Strait of Hormuz closed, driving oil prices higher.
The latest exchanges mark a sharp escalation in both the pace and geographic reach of attacks over the past week, casting doubt on an interim US-Iranian agreement signed last month to reopen the strait and halt hostilities while the sides pursued a further 60 days of negotiations.
