US President Donald Trump has condemned Iran as a "fanatical regime" and refused to continue certifying a landmark international nuclear deal.
He accused Iran of sponsoring terrorism and said he would deny the regime "all paths to a nuclear weapon".
International observers say Iran has been in full compliance with the 2015 deal freezing its nuclear programme.
Iranian President Hassan Rouhani said the US was "more than ever isolated" and could not change the nuclear deal.
"As long as our rights are guaranteed, as long as our interests are served, as long as we benefit from the nuclear deal, we will respect and comply with the deal," Mr Rouhani said.
Mr Trump said the deal was too lenient, and Iran had "committed multiple violations of the agreement". Iran, he said, was spreading "death, destruction and chaos".
It was "not living up to spirit of the deal", he said, but receiving the benefit of sanctions relief regardless. His new strategy would fix that, he said.
The US reserved the right to leave the deal at any time, he warned, and would do so unless "satisfactory" changes were made.
Mr Trump had been under pressure at home and abroad not to scrap the deal, signed in July 2015 by Iran and the US, UK, France, China and Russia plus Germany.
How did key players respond?
Yukiya Amano, head of the International Atomic Energy Agency (IAEA), said Iran was implementing the deal and was subject to "the world's most robust nuclear verification regime".
That view was reinforced by EU foreign policy chief Federica Mogherini, who said the deal was "robust" and that there had been "no violations of any of the commitments in the agreement".
It was not in the power of "any president in the world" to terminate the agreement, which had been established by a UN Security Council resolution, she said.
In a joint statement, the UK, Germany and France said they were "concerned" by Mr Trump's move but remained committed to the deal. But they added they also "shared concerns about Iran's ballistic missile programme and regional activities".
Russia also remained committed to the deal and was opposed to the use of "aggressive and threatening rhetoric in international relations".
Israeli Prime Minister Benjamin Netanyahu congratulated Mr Trump, who he said had "boldly confronted Iran's terrorist regime". Saudi Arabia also backed the US president's "firm strategy".
What has changed?
By Lyse Doucet, chief international correspondent
President Trump has recast the list of Middle East threats, with Iran replacing Islamic State as Enemy Number One.
That world view is shared by his strongest supporters in the region, including Israel and Gulf Arab leaders who have long seen Iran as their primary threat, and a rival with vast sway across the Middle East.
They resented Washington's focus on the Iran deal during President's Obama administration. Like President Trump, they want to undo his legacy. The new approach imposes new sanctions but stops short of designating Iran's elite Revolutionary Guards as a terrorist group – a step Iran says would be tantamount to a declaration of war.
The urgent question now is whether the new strategy will embolden Iran's hardliners including the Revolutionary Guards. Like US forces, they're involved in battles to defeat IS in Iraq and Syria, and may also see a new enemy.
What violations of the nuclear deal did Mr Trump say Iran had committed?
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Image caption Worshippers shouted anti-US slogans during Friday prayers in Tehran
On two occasions, he said, they had exceeded the limit of 130 tonnes of heavy water (a source of plutonium suitable for a nuclear bomb).
Until recently, he said, the regime had failed to meet expectations in its operation of advanced centrifuges.
He claimed it had also "intimidated international inspectors into not using the full inspection authorities that the agreement calls for".
What changes does Trump want?
Among the changes he is seeking is the end to the nuclear deal's "sunset" clauses, one of which sees the lifting of restrictions on Iran's nuclear enrichment programme after 2025.
Mr Trump also focused on the activities of the Revolutionary Guards, which he called the "corrupt personal terror force of Iran's leader", and Iran's missile programme, which he said threatened "global trade and freedom of navigation".
A key criticism of the Iran deal by Mr Trump has been that it fails to cover Iran's ballistic missile programme. Last month, Iran successfully tested a new medium-range missile with a 2,000km (1,200-mile) range.
Mr Trump said he would impose sanctions outside the Iran deal targeting both