Iran has faced increased USA pressure and possible sanctions since Mr Trump's decision in May to withdraw the U.S. from a 2015 global agreement over Teheran's nuclear programme.
However, at least as of last week, the Pentagon said those Iranian threats had not led the US military to reposition or add to forces in the Middle East.
James Jay Carafano, a national security specialist at The Heritage Foundation, said the president was expressing himself to Tehran "in a uniquely Trumpian manner".
Although Iran and European signatories have been scrambling to save the deal, many Western companies and banks have stopped doing business in Iran amid fears they could be targeted by a reapplication of United States sanctions.
Following the U.S. withdrawal from the Iran nuclear accord that stunned even Washington's closest European allies, Pompeo on May 21 unveiled a "new strategy" meant to force Iran to yield to a dozen stringent demands.
"I don't think that's warranted".
It's tempting to compare Trump's Iran strategy to his "madman" North Korea strategy, given he pledged to "totally destroy" and inflict "fire and fury" upon Kim Jong Un's regime before sitting down at the negotiating table. "I wouldn't recommend that", he said.
As for the denizens of the internet, they've responded to the President's threat in the only way they know how.
Israeli Prime Minister Benjamin Netanyahu praised Mr Trump's "strong stance" on Iran. Iranian hackers, meanwhile, were planning extensive cyberattacks on USA and European targets, prompting consideration of a US counterattack, multiple senior US officials told NBC News. "And Iranians have heard them - albeit more civilized ones - for 40 yrs".
"Neither Iran, nor any other country is interested in escalating tensions in the region", he said.
In a blistering speech earlier Sunday evening, US Secretary of State Mike Pompeo likened the Iranian regime to the mafia, accusing the clerics that rule the country of enriching themselves and funding terrorism at the expense of ordinary Iranians. "And the United States under President Trump will not stay silent either".