The ayatollahs in Iran needed to hear Donald Trump get tough, the President's national security adviser has told Sky News.
John Bolton hailed Mr Trump's "outstanding speech" in which he pulled the US out of the Iran nuclear deal.
"It was very direct, very clear, very tough. That's what the ayatollahs needed to hear," Mr Bolton said.
During his White House announcement on Tuesday, Mr Trump called the Joint Comprehensive Plan of Action (JCPOA) "disastrous" and "one-sided".
He said no action taken by Iran had been more dangerous than its pursuit of nuclear weapons, and claimed the deal had allowed Iran to enrich uranium and "cause havoc within the Middle East and beyond".
The 2015 agreement was made by Iran and the US, the UK, Russia, France, China, Germany and the EU to ensure Iran's nuclear programme was "exclusively peaceful".
In return, the US agreed to lift a range of nuclear-related sanctions, which Mr Trump will now reimpose.
Speaking to Sky News after the President's announcement, Mr Bolton allayed concerns from the international community about the decision.
He said the US would work with its European allies, "particularly Britain, France and Germany" to construct an answer to the larger threat from Iran and "not just the nuclear weapons programme".
A new solution would address Iran's "support for terrorism, their disruptive military operations across the region and all of their malign influence".
He added the President's move is "part of really dealing with Iran".
Under the deal, spearheaded by Barack Obama, Iran stopped producing 20% enriched uranium and gave up the majority of its stockpile in return for most international sanctions on it being lifted.
But Iran's president Hassan Rouhani warned that Iran was ready to resume its nuclear activities if its interests were not guaranteed under a deal without the United States.
"If needed, we will resume our nuclear enrichment at the industrial level without any limit," he said.
Mr Bolton said he understands why some in the international community are not optimistic about the future, but he said the deal was not an effective way of stopping Iran from getting nuclear weapons.
"I have been involved in a lot of arms control negotiations in my day and I can tell you that this deal was not going to stop Iran from getting nuclear weapons.
"We have a legitimate disagreement with our friends in Europe," he said, "but we are going to try now to work beyond this deal and I am optimistic that we can make progress".
Mr Trump was castigated by many foreign leaders for his decision, as well as by his Democratic predecessor.
The Iran deal was seen as one of the Obama administration's key foreign policy achievements.
"I believe that the decision to put the JCPOA at risk without any Iranian violation of the deal is a serious mistake," the former president said in a statement.
"Without the JCPOA, the United States could eventually be left with a losing choice between a nuclear-armed Iran or another war in the Middle East.
"We all know the dangers of Iran obtaining a nuclear weapon. It could embolden an already dangerous regime; threaten our friends with destruction; pose unacceptable dangers to America's own security; and trigger an arms race in the world's most dangerous region."
Prime Minister Theresa May, in a joint statement with France's Emmanuel Macron and German Chancellor Angela Merkel, expressed her "regret and concern" and urged "all sides to remain committed" to the deal.
"Together, we emphasise our continuing commitment to the JCPOA," their statement read.
"This agreement remains important for our shared security."
Russia's deputy UN ambassador Dmitry Polyanskiy said Moscow was "disappointed" but "not surprised" by the move.
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Despite the opposition, Israeli Prime Minister Benjamin Netanyahu praised the "brave and correct" decision by Mr Trump, before saying the 2015 accord was a "recipe for disaster".
According to the US Treasury, sanctions related to Iran's energy, auto and financial sectors will be reimposed in three and six months.