But the angst in Berlin, Brussels, London and Paris underlined what is at stake: the mercurial USA president is quite capable of sabotaging the agreement.
It is aimed at ensuring Iran uses its nuclear capabilities for peaceful purposes while preventing it from gaining nuclear weapons.
The US still maintains sanctions on Iran - independent of the nuclear deal - on matters such as terrorism, human rights and ballistic missile development. The next sanctions waivers are due in May.
Trump extended the waivers of key sanctions that were lifted as part of the Obama-era agreement Friday, but he said it was the last time.
If he does allow the punitive measures to go back into effect, Iran will accuse the United States of breaking the deal, under which Tehran accepted restrictions on its nuclear program. He also called on Iran to stay calm and continue to fulfil obligations under the deal.
European allies had strongly urged the White House to stick with the nuclear deal, saying a decision to abandon it would strain the transatlantic partnership.
French President Emmanuel Macron called Trump on Thursday and stressed France's determination to see "the strict application of the deal and the importance of all the signatories to respect it".
"We are gradually coming to the conclusion that an internal decision by the USA to leave the (Joint Comprehensive Plan of Action) has already been made or is close to being made", Ryabkov said in an interview with Interfax news agency.
"Is he bluffing? I don't think so".
Iranian Foreign Minister Mohammad Javad Zarif on Saturday said the world direly needs a cultural dialogue for security of all in Asia. The appeal was made after the Iranian Foreign Minister met with European Union foreign ministers and European Union foreign policy chief Federica Mogherini in Brussels on Thursday.
In his statement Friday, Trump said he remained open to revising the Iran Nuclear Agreement Review Act, or INARA.
Iran has said that if the USA walks away from the agreement, it is ready to give an "appropriate and heavy response".
One of the criticisms levelled at the nuclear deal is that it does nothing to address Iran's continuing ballistic missile program and involvement in conflicts such as Yemen and Syria.