“As we have seen in North Korea, the longer we ignore a threat, the worse that threat becomes.

“It is why we are determined that the world’s leading sponsor of terrorism will never obtain nuclear weapons.”

The intervention - which marks a major shift in America’s Iranian policy - was criticised by a string of world leaders.

The statement from Mrs May, Mrs Merkel and Mr Macron read: “We stand committed to the JCPoA and its full implementation by all sides. Preserving the JCPoA is in our shared national security interest."

The EU's top diplomat Federica Mogherini said that the Iran nuclear deal was "working and delivering", insisting Mr Trump did not have the power to terminate it.

"We cannot afford as an international community, as Europe for sure, to dismantle an agreement that is working and delivering,” she said.

Israel Katz, Israel's intelligence minister, said: “I think that the speech was very significant. Iran is the new North Korea. We see where things are goings.”

However other figures in the Middle East - including Israel’s Prime Minister Benjamin Netanyahu and leaders in Saudi Arabia - welcomed the move.

These so-called “trigger points” are expected to include Iran’s nuclear behaviour but also its ballistic missile testing - something not covered in the initial agreement.

The changes will be proposed in an amendment to the Iran Nuclear Agreement Review Act - a piece of US legislation.

Mr Tillerson said the decision was part of a comprehensive review of Iran’s behaviour, including its links to terrorism in the regime.

The US administration will also attempt to disrupt funding to parts of the Islamic Revolutionary Guard Corps, which America claims is helping terrorist groups.

A White House spokesman said: “The United States’ new Iran strategy focuses on neutralising the government of Iran’s destabilising influence and constraining its aggression, particularly its support for terrorism and militants.

“We will revitalise our traditional alliances and regional partnerships as bulwarks against Iranian subversion and restore a more stable balance of power in the region.”