In an expletive-laden post Sunday morning, Trump promised the "crazy bastards" would be "living in Hell" if the waterway isn't opened to marine traffic.
Trump had previously threatened strikes two weeks ago, but extended the deadline for Iran to reopen the waterway twice, claiming there were positive signs in negotiations with the Iranians.
But there have been few public signs of progress in a diplomatic off-ramp to the war.
The president's latest tirade came after he said a US service member who had been missing since Iran shot down a fighter jet had been rescued.
A frantic US search-and-rescue operation unfolded after the crash of the F-15E Strike Eagle jet on Friday, as Iran also promised a reward for anyone who turned in the "enemy pilot".
A second crew member was rescued earlier.
Trump wrote in a social media post that the aviator is injured but "will be just fine", adding that he took refuge "in the treacherous mountains of Iran".
"This brave Warrior was behind enemy lines in the treacherous mountains of Iran, being hunted down by our enemies, who were getting closer and closer by the hour," Trump wrote.
But the announcement was disputed by spokesperson for the Khatam al-Anbia Central Headquarters, Colonel Ebrahim Zolfagari, who said that Iranian military forces thwarted the rescue mission, downing several US aircraft in the process, according to Tasnim news agency.
The operation resulted in the destruction of multiple hostile aircraft, including two Black Hawk helicopters and one C-130 military transport plane, all of which were struck and left burning in southern Isfahan, said the spokesman cited by Tasnim.
Trump said the rescue involved "dozens of aircraft" and the US had been monitoring the airman's location "24 hours a day, and diligently planning for his rescue".
The fighter jet was the first US aircraft to have crashed in Iranian territory since the conflict began in late February.
In a separate incident, ​an A-10 Warthog fighter aircraft was hit and crashed over Kuwait, with the pilot ejecting, US officials said.
Two Black Hawk helicopters that engaged in the search for the missing US air crew member were hit by Iranian fire but made it out of Iranian airspace, the US officials told Reuters.
Earlier, Trump posted on his social media platform that Iran had 48 hours to open the Strait of Hormuz before "all Hell will reign (sic) down on them".
General Ali Abdollahi Aliabadi of Iran's joint military command responded with "the doors of hell will be opened to you" if Iran's infrastructure is attacked, state media reported, with the general threatening all infrastructure used by the US military in the region.
The war, now in its sixth week, began with joint US-Israel strikes on February 28 and has killed thousands, shaken global markets, cut off key shipping routes and spiked fuel prices.
In an apparent move to heap further pressure on Tehran following Trump's latest ultimatum, a senior Israeli defence official said Israel was preparing to attack Iranian energy facilities in the next week, and was awaiting approval from the US.
"We will continue to crush them," Israeli Prime Minister Benjamin Netanyahu said of the Iranian regime on Saturday.
Israel's military confirmed it struck a petrochemical complex in Iran's Mahshahr that Netanyahu said helps to fund the war.
Five people were killed and 170 more were injured, Iranian state media reported, citing a provincial security official.
The Atomic Energy Organisation of Iran said an airstrike hit near its Bushehr nuclear facility, killing a security guard and damaging a support building.
The head of Russia's state nuclear corporation, Rosatom, said 198 workers were being evacuated. It was the fourth time the facility was targeted.
Pakistan's Foreign Ministry spokesperson, Tahir Andrabi, told The Associated Press his government's efforts to broker a ceasefire are "right on track" after Islamabad last week said it would soon host talks between the US and Iran.
Iran's foreign minister, Abbas Araghchi, said Iranian officials "have never refused to go to Islamabad".
Mediators from Pakistan, Turkey and Egypt were working to bring the US and Iran to the negotiating table, according to two regional officials.
With AP
