When it comes to avoiding the frightening prospect of an all-out military confrontation between the the two countries, the world's best hope is that Trump's instincts continue to prevail.
Unlike other members of his administration, such as his neo-conservative national security adviser John Bolton, Trump is an isolationist at heart. He wants the era of US military adventurism to end.
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"What will we get for bombing Syria besides more debt and a possible long term conflict?" he said back in 2013.
Just this week, when asked about Iran, he told Time magazine: "I’d like to get out of the Middle East, we should have never been in the Middle East. We should have never been there, and I’d like to get out."
Since entering the White House, Trump has engaged in hairy-chested rhetoric - threatening the "official end" of Iran and promising to rain down "fire and fury" on North Korea.
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This bellicose language, and his tendency to behave impulsively, has fuelled concerns about the potential damage he could do to global peace and security.
Remember Hillary Clinton's warning in the 2016 presidential election campaign: "A man you can bait with a tweet is not a man we can trust with nuclear weapons."
Thankfully, however, Trump's actions have rarely matched his words.
Trump's backdown disappointed some more gung-ho Republicans, who said it reminded them of Barack Obama's foreign policy fecklessness. But it came as a relief to many more Americans who do not want to see the US-Iranian hostilities morph into a major confrontation.
As Obama's defence secretary Leon Panetta said on Friday, it is important for Iran to know that it cannot act with impunity. But he added: "I would be careful about starting war over a drone."
More broadly, though, it is impossible to be complimentary about Trump's approach to Iran since he took office.
The seeds for the current crisis were sown last year when Trump unilaterally withdrew the US from Obama's landmark Iranian nuclear deal.
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In doing so he went against the advice of his top foreign policy officials and several of America's closest allies including the UK and the European Union.
The agreement didn't achieve all America's strategic aims for Iran, like ending its support for Islamic terrorist groups around the world. But it did constrain Iran's nuclear ambitions and decreased the likelihood of military confrontation.
Trump could have tried to strengthen the deal and extract more concessions from Iran. But that would have required patient negotiations and a willingness to build on Obama's achievements.
Instead, he tore the whole thing up.
It's no surprise Iran eventually responded by lashing out, first by allegedly attacking two tankers in the Gulf of Oman and then by shooting down the US drone.
While the reintroduction of US sanctions has crippled Iran's economy, it's unclear what the Trump administration's strategic end game is - besides unrealistic dreams of regime change.
It hasn't helped that Trump has gone six months without appointing a permanent Defence Secretary following the resignation of the respected James Mattis just before Christmas.
The acting secretary, Patrick Shanahan, this week announced he was withdrawing from the nomination process following reports of multiple instances of domestic violence in his family.
This has created a leadership vacuum at the Pentagon at a critical time and deprived Trump of the fearless advice he needs.
While it's a relief Trump called off military action this time, the situation remains extremely volatile.
It's easy to imagine Iran and the US stumbling into a war unless they find a way to cool things down and return to the negotiating table.
Matthew Knott a reporter for The Sydney Morning Herald and The Age based in the United States.