The global reach of the USA financial system and the US presence of many European companies also raise questions about its effectiveness.
And Germany said it will spend the next few months trying to persuade Washington to change its mind.
On Sunday, John Bolton, National Security Adviser, appeared on the CNN's State of The Union and hinted that the USA wouldn't think twice about imposing sanctions on its allies if they continue to help Iran.
This left dismayed European allies scrambling to salvage the global nuclear pact as Tehran said Trump had made a mistake and proved Washington could not be trusted.
Global benchmark Brent crude stabilised near 3-1/2-year highs on Friday as the prospect of new United States sanctions on Iran tightened the outlook for Middle East supply at a time when global crude production is only just keeping pace with rising demand.
Rouhani said earlier in the week that Iran would remain in the 2015 pact, also known as the Joint Comprehensive Plan of Action (JCPOA). On Saturday, French President Emmanuel Macron told Trump in a telephone call that he was anxious about stability in the Middle East, according to Macron's office.More news: Chili's announces breach in systems
More news: Allardyce sets Everton transfer rumour straight - 'Let's put this right'
More news: Doctors grow ear transplant inside soldier's arm
Ayatollah Ahmad Khatami, a member of Iran's clerical elite, was not in a conciliatory mood at a protest in Tehran, accusing the United States of treachery. However in an interview aired on the ABC's This Week, Bolton said refused to confirm his personal views.
Basravi said the Rouhani government's "political health. hangs in the balance" as the administration has "married itself to this deal and championed it as the answer to all" of the country's economic woes.
China's Foreign Ministry on May 13 said Zarif will "exchange views with relevant parties on the developments of the Iranian nuclear issue".
In a statement published Friday, Iranian Foreign Minister Javad Zarif said he would embark on a round of worldwide diplomacy to try and save the deal.
Germany and France said they would seek to shield European companies from US sanctions, which would prohibit companies that do business in Iran from using the USA financial system.
Russian Federation has also criticised Trump's decision, with Kremlin spokesperson Dmitry Peskov alleging the move was "protectionism in disguise", in comments made on Thursday to state news agency TASS.
"I think at the moment there's some feeling in Europe - they're really surprised we got out of it, really surprised at the reimposition of strict sanctions".