European Union foreign policy chief Federica Mogherini said European Union experts were aiming to come up with concrete proposals in the coming weeks on nine key issues including ensuring Iran could sell its oil and gas products and have access to worldwide finance.
"But if we want to stay in this agreement and ensure that Iran stays in this agreement and abides to the terms of the agreement, then we need to talk about this", German Foreign Minister Heiko Maas said.
The European powers share Trump's concerns but say that the nuclear deal is the best way to prevent Tehran from obtaining an atomic weapon.
The Europeans and Iranians have now tasked experts to come up with measures quickly and will meet again in Vienna next week at a deputy foreign minister level.
"The Europeans, after the withdrawal of the U.S. from the deal, have found themselves forced to save the Joint Cooperative Plan of Action themselves", he added.
Accordingly, Iran's President Hassan Rouhani said that Iran would remain in the global nuclear deal in case the country's interests are secured by other parties to the agreement.
"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.
"I think the Europeans will see that's in their interest ultimately to go along with this", he said.
"We are working on the measures that we can start to put in place, and we will look at the content of that", she said.
"So, we are not talking about annexes or modifications of the agreement at all; we are talking about setting up concrete measures, concrete practical solutions to address these issues, which could take different forms depending on the different issues covered - but something very concrete, very practical and hopefully very operational and very quickly", the European Union top diplomat went on.
Chinese Foreign Ministry spokesman Geng Shuang added: "China is highly concerned with the direction of the Iranian nuclear issue and is willing to maintain communication with all relevant parties, including Iran".
White House national security adviser John Bolton said Sunday that "it's possible" there will be secondary sanctions imposed on European companies as a result of the U.S. withdrawal from the Iran nuclear deal.
The US has given all firms, not just European ones, between three and six months to wind down their business dealings with Iran, with the timeframe dependent on the nature of the business. Following Trump's decision, the Treasury Department's Office of Foreign Assets Control sanctioned nine Iranian individuals and entities including those with links to Iran's Revolutionary Guard.
They include retaliatory sanctions, allowing the European Investment Bank to invest directly in Iran and coordinating euro-denominated credit lines from European governments.
"We have to accept, be realistic about the electrified rail, the live wire of American extraterritoriality and how that can serve as a deterrent to businesses", Johnson said.
Iran has said it is preparing to resume "industrial-scale" uranium enrichment "without any restrictions" unless Europe can provide solid guarantees that it can maintain trade ties despite renewed United States sanctions.
German exports to Iran totalled almost €3bn (£2.6bn) in 2017, while French exports soared from €562m in 2015 to €1.5bn in 2017.