The EU says it will stick to the deal as long as Iran keeps to its commitments, and the coming days and weeks will be crucial in persuading Tehran to stay on board.
What happens next?
Britain, France and Germany -- the three European signatories to the deal collectively known as the E3 -- have launched a diplomatic push to reassure Iran of their commitment to the deal.
French President Emmanuel Macron spoke to his Iranian counterpart Hassan Rouhani on Wednesday, and the pair agreed to work toward "the continued implementation of the nuclear deal".
Foreign ministers from the European trio are to meet representatives of Tehran on Monday and the Iran deal will also feature at an EU summit in Sofia next week.
European powers will also speak to China and Russia, the deal's other signatories, to coordinate their response, though an EU diplomat said it would be wrong to characterise it as an attempt to "isolate" Washington.
But while these political gestures are important, Iran has demanded concrete assurances that trade will be protected.
"We have to talks about incentives for Iran to stay in the agreement. This means that we need to find means to absorb the economic shock of reimposing sanctions by the US," an EU diplomat told AFP.
Strategy
London, Berlin and Paris have kept details of their strategy under wraps, but a report by the International Crisis Group (ICG) think tank outlined steps that could reassure businesses working with Iran and help moderate Iranian leaders persuade hardliners to stick with the deal.
EU states could use their state investment agencies to cover risks such as sanctions that companies could face in trading with Iran, ICG suggested, while the E3 could launch a joint effort to support Iranian infrastructure projects through their development agencies.
Another option, and one spoken of by European officials in recent weeks, would be to make Iran eligible for loans from the European Investment Bank (EIB) -- thereby giving Tehran access to international finance in euros to sidestep US sanctions on dollar transactions.
"You can try to do business in other currencies like the euro, but you need banks that are active in this field," an EU diplomat said.
"For banks who do business in the US, this is not easy. That's why we think about the EIB."
But former French foreign minister Hubert Vedrine warned that bypassing dollar transactions would be "very, very, very difficult in the real world".
What about the 'blocking statute'?
There has been talk in Brussels that the EU could counter US sanctions by adapting a 1996 regulation originally created to get around Washington's trade embargo on Cuba.
This so-called "blocking statute" prohibits EU companies and courts from complying with specific foreign sanctions laws and says no foreign court judgments based on these laws have any effect in the EU.
But the row with the US over the Cuba embargo was settled politically, so the effectiveness of the blocking regulation has never been put to the test.
An EU source acknowledged that the "political symbolic effect is potentially bigger than the economic effect".
"If a company is active on the large American market and small Iranian market, then it does not benefit much from the fact that its European and Iranian business is protected but not its activities in the US," the source said.
'Chilling effect'
Washington has granted a six-month grace period for businesses to wind down operations in Iran before reimposing sanctions, but at this early stage there is already scepticism about the effectiveness of any countermeasures that the EU and its allies might take.
The foreign policy chief of German Chancellor Angela Merkel's party, Norbert Roettgen, said businesses would simply not want to run the risk of falling foul of the US.
"Whoever invests in Iran will be hard hit by US sanctions, and that cost can't be offset," he told Der Spiegel magazine.
"So the affected companies will probably very quickly roll back their investments or pull out of the country altogether."
Even before Trump's announcement, EU officials admitted they were already seeing "a chilling effect on business operators".
But Mark Fitzpatrick, executive director for the International Institute for Strategic Studies, argued that efforts to pursue an alternative deal without the US could lead to a shake-up of the global power dynamic.
"Some countries, they're just going to ignore the United States' threat. China isn't going to kowtow to the United States on this, and so the Europeans might see how China fares in resisting US pressure on Iran," he told AFP.
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