He said a US navy guided missile destroyer in the Gulf of Oman stopped the Iranian vessel by blowing a hole in its engine room.
"We have full custody of their ship, and are seeing what's on board!" he wrote on social media.
There was no immediate Iranian comment.
The news threw into question Trump's earlier announcement that US negotiators would head to Pakistan on Monday for another round of talks with Iran.
That had raised hopes of extending a fragile ceasefire set to expire by Wednesday although an Iranian state news agency reported Iranian officials did not plan to take part in the talks.
"Iran stated that its absence from the second round of talks stems from what it called Washington's excessive demands, unrealistic expectations, constant shifts in stance, repeated contradictions, and the ongoing naval blockade, which it considers a breach of the ceasefire," Iran's official IRNA news agency said.
The United States has kept a blockade of Iranian ports in place, while Iran has lifted and then reimposed its own blockade of marine traffic through the Strait of Hormuz, which before the war began almost two months ago handled roughly one-fifth of the world's oil supply.
Iran's announcement that it would walk away from negotiations came after Trump said his envoys would arrive in Islamabad on Monday evening, one day before a two-week ceasefire ends.
A White House official had said the US delegation would be headed by Vice President JD Vance, who led the war's first peace talks a week ago, and also include Trump's envoy Steve Witkoff and son-in-law Jared Kushner.
The apparent diplomatic setback could set the stage for a renewed surge in oil prices when markets reopen after the weekend.
Now in its eighth week, the war has created the most severe shock to global energy supplies in history, sending oil prices surging because of the de facto closure of the strait.
Iran's chief negotiator, Mohammad Baqer Qalibaf, earlier said the two sides had made progress but were still far apart on nuclear issues and the Strait of Hormuz.
Two giant US C-17 cargo planes landed at Pakistan's Nur Khan air base on Sunday afternoon carrying security equipment and vehicles in preparation for the US delegation's arrival, two Pakistani security sources said.
City authorities in the capital Islamabad halted public transport and heavy goods traffic through the city.
Rolls of barbed wire were rolled out near the Serena Hotel where last week's talks were held and the hotel told all guests on Sunday to leave.
Pakistan has served as the main mediator, and Prime Minister Shehbaz Sharif spoke by phone on Sunday with Iran's President Masoud Pezeshkian.
Sharif's office said Pezeshkian had thanked Pakistan for its mediation efforts, in a readout of the call that made no mention of Iran rejecting the next round of talks.
with AP
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