Rafael Mariano Grossi - Director General of the International Atomic Energy Agency (IAEA) is preparing to fly to Iran to inspect the country's nuclear facilities, unless new restrictions imposed by Iran prevent it.
European parties to the deal, which have called on Tehran not to halt snap inspections, will discuss the issue with the United States on Thursday, the French Foreign Ministry said.
The new U.S. administration under President Joe Biden has said it wants to return to the JCPoA if Iran first recommits to its own obligations.
"We're obviously concerned about the risk of further non-compliance by Iran with the JCPOA", British Foreign Secretary Dominic Raab said after the talks.
Tehran retaliated by stepping up nuclear work in violation of the accord.
"The E3 and the United States affirmed their shared objective of Iran's return to full compliance with its commitments under the JCPOA", the statement said.
"The E3 and the United States are united in underlining the unsafe nature of a decision to limit IAEA access, and urge Iran to consider the consequences of such grave action, particularly at this time of renewed diplomatic opportunity".
Iranian Foreign Minister Mohammad Javad Zarif was quick to hit back at the statement, saying Iranian breaches to the pact were merely a result of Washington's withdrawal from it.
"These activities have no credible civil justification", it said, "Uranium metal production is a key step in the development of a nuclear weapon".
Refining uranium to high levels of fissile purity is a potential pathway to nuclear bombs, though Iran has long said it its enrichment program is for peaceful energy purposes only. The 2015 deal says Iran can only enrich with far less efficient, first-generation IR-1 centrifuges.
He tweeted: "Instead of sophistry and putting onus on Iran, E3/EU must abide by own commitments and demand an end to Trump's legacy of economic terrorism against Iran".
"Our remedial measures are a response to US/E3 violations". "We'll follow ACTION w/ (with) action".
"Apparently Iran is not interested in easing the tensions, but in escalation".
The Additional Protocol permits IAEA inspectors to visit undeclared sites in Iran at short notice, but on 15 February, Iran's Ministry of Foreign Affairs said it would cancel this commitment if there was no progress by the end of this month in Tehran's dispute with the US over the re-imposition of economic sanctions by the previous administration under Donald Trump.
German Chancellor Angela Merkel and the president of the European Council spoke with Iranian President Hassan Rouhani this week to try to end the diplomatic standoff.
Following reports of Merkel's phone call, Iran's supreme leader, Ayatollah Ali Khamenei, responded with counterdemands of "action, not words" from the United States if it really wants to revive the agreement.
Rouhani - a key advocate of nuclear diplomacy with global powers - is set to step down after serving the maximum two consecutive terms, and a more hardline figure is likely to replace him.
This would involve Washington revoking Trump's 2018 withdrawal and green-lighting an Iranian request for an emergency International Monetary Fund loan, while Iran freezes "the most problematic aspects" of its nuclear programme, he said.
Iranian officials, however, say that Washington - as the party that left the JCPOA - must make the first move.