In his first public comments after the 21-hour talks, Trump sought to eliminate Iran's key source of leverage in the war by exerting strategic control over the waterway that was responsible for the shipping of 20 per cent of global oil supplies before fighting began.
A US blockade could further rattle global energy markets.
It was not immediately clear how it might be carried out, but Trump told Fox News the goal was to ensure all ships could transit: "It's going to be all or none, and that's the way it is".
Trump said he has "instructed our Navy to seek and interdict every vessel in International Waters that has paid a toll to Iran. No one who pays an illegal toll will have safe passage on the high seas."
Other nations would be involved in the blockade, he said, but did not name them.
Freedom of peaceful navigation is a basic principle of international maritime trade, but Iran has asserted control of the strait.
Iran's Revolutionary Guard later said the strait remained under Iran's "full control" and was open for non-military vessels, but military ones would get a "forceful response," two semi-official Iranian news agencies reported.
During the talks, the US military said two destroyers had transited the strait ahead of mine-clearing work, a first since the war began. Iran denied that.
Trump stressed that Tehran's nuclear ambitions were at the core of the talks' failure, and the US was ready to "finish up" Iran at the "appropriate moment".
In comments to Fox News, he again threatened to strike civilian infrastructure and said he was fine with his widely criticised threat before the ceasefire that a "whole civilisation will die tonight".
The face-to-face talks that ended early Sunday were the highest-level negotiations between the longtime rivals since the 1979 Islamic Revolution. Both delegations later left Islamabad.
Each side had earlier blamed the other for the failure of talks to end six weeks of fighting that has killed thousands, roiled the global economy and sent oil prices soaring.
Neither indicated what will happen after the ceasefire expires on April 22.
"We need to see an affirmative commitment that they will not seek a nuclear weapon, and they will not seek the tools that would enable them to quickly achieve a nuclear weapon," Vice President JD Vance, leading the U.S. side, said afterwards.
Iran's Parliamentary Speaker Mohammad Baqer Qalibaf, who led his country's delegation along with Foreign Minister Abbas Araqchi, blamed the US for not winning Tehran's trust despite his team offering "forward-looking initiatives".
"The US has understood Iran's logic and principles and it's time for them to decide whether they can earn our trust or not," Qalibaf said on X.
Pakistani Foreign Minister Ishaq Dar said his country will try to facilitate a new dialogue in the coming days.
Since the US and Israel launched the war on February 28, it has killed at least 3000 people in Iran, 2020 in Lebanon, 23 in Israel and more than a dozen in Gulf Arab states, and caused lasting damage to infrastructure in half a dozen Middle Eastern countries.
