Donald Trump has announced new sanctions against Iran after Tehran threatened to enrich its stockpile of uranium.
The US president has issued an executive order imposing new restrictions on Iranian steel, aluminium, copper and iron.
Those sectors provide Iran’s troubled economy with foreign currency earnings.
Mr Trump said Tehran could expect “further actions unless it fundamentally alters its conduct”.
He said in a statement: “Today’s action targets Iran’s revenue from the export of industrial metals – 10% of its export economy – and puts other nations on notice that allowing Iranian steel and other metals into your ports will no longer be tolerated.”
Iran threatened to enrich its stockpile of uranium closer to weapons-grade levels in 60 days if world powers failed to negotiate new terms on the 2015 nuclear deal.
President Rouhani’s words come exactly a year after Donald Trump withdrew America from the Obama-era agreement and reimposed sanctions, although other nations stayed in.
Mr Rouhani issued the ultimatum to the remaining signatories of the deal – Britain, China, the European Union, France and Germany.
State television said letters outlining the partial withdrawal from the deal had been sent to the countries’ ambassadors, and also to Russia.
Mr Rouhani said Iran would stop exporting excess uranium and heavy water from its nuclear programme, two requirements of the deal.
He did not give details on the extent to which Iran was prepared to enrich uranium.
“This surgery is to save the [deal], not destroy it,” Mr Rouhani said.
“If the five countries join negotiations and help Iran to reach its benefits in the field of oil and banking, Iran will return to its commitments according to the nuclear deal.”
Earlier, Foreign Secretary Jeremy Hunt said there would be “consequences” for Iran if it broke its commitments under the 2015 deal.
Mr Hunt, speaking alongside US Secretary of State Mike Pompeo, described Iran’s threat to increase uranium enrichment as an “unwelcome step”.
He urged Iran “not to take further escalatory steps and to stand by its commitments”.
Mr Pompeo said he was confident America and its allies would ensure Iran had “no pathway for a nuclear weapons system”.