Technical experts from both sides were commissioned to find ways to maintain oil shipments and to protect European companies doing business with Iran, EU foreign policy chief Federica Mogherini told reporters in Brussels late on Tuesday.
The foreign ministers of Britain, France, Germany and Iran will hold talks in Brussels on Tuesday to discuss saving the deal.
Iran's foreign minister on Tuesday hailed talks with the European Union to try to find a way to rescue the Iran nuclear deal after the U.S. pulled out as a "good start".
All parties to the deal are due to meet in Vienna for talks at the level of political directors, Mogherini announced.
Bolton also reiterated the administration's objection to the sunset provisions in the Iran deal, which President Donald Trump called "totally unacceptable".
"It is not the matter of Iran's nuclear deal, it is the matter of dignity of Europe because President Trump believes in unilateralism; he thinks he's master of the world, he's a business police of the world and he will make a decision and the other countries must obey him", Mr Mianji said.
The European Commission has been examining measures to counter the introduction of any USA sanctions that might harm European businesses and is expected to unveil them to EU leaders at a summit in Sofia, Bulgaria, on Wednesday. "That is clear to us all", he said.
The White House said Trump had spoken with French President Emmanuel Macron on Saturday and "reiterated the need for a comprehensive deal that addresses all aspects of Iran's destabilizing activity in the Middle East".
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Bolton said Europe was still digesting Trump's May 8 move. "I think that will sink in; we'll see what happens then", Bolton said. The U.S. decision reignited the danger of economic crisis for Iran, which is now at the center of Tehran's diplomatic efforts .
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Minister for trade and export David Parker last week said it was still unclear to the nations who remained in the nuclear agreement what exports or trade were at risk when associating with Iran.
Trump's decision to reimpose Iran-related sanctions would act as an "electrified rail" to those wanting to do business with the country, his British counterpart Boris Johnson added.
The deal between Iran and six world powers lifted most global sanctions in 2016 in return for Tehran curbing its nuclear programme, under strict surveillance by the United Nations, to stockpile enriched uranium for a possible atomic bomb.
The United States threatened on Sunday to impose sanctions on European companies that do business with Iran, as the remaining participants in the Iran nuclear accord stiffened their resolve to keep that agreement operational.
Major European powers sought Tuesday to keep Iran committed to a deal to prevent it from building a nuclear bomb despite deep misgivings about Tehran's Middle East politics and President Donald Trump's vehement opposition.
She added: "Britain, France and Germany were of the opinion that the agreement against Iran's nuclear armament is an agreement that certainly has weaknesses, but an agreement we should stand by".
German exports to Iran totaled almost 3 billion euros ($2.3 billion) in 2017, while French exports soared from 562 million euros ($670 million) in 2015 to 1.5 billion ($1.8 billion) in 2017 and oil giant Total has pledged to invest some $5 billion in the South Pars gas field.
"Today we hope to see how we can use the available mechanisms not to allow the undermining of this important document with the participation of European Troika, China, Russia, Iran and European Union", he stressed.