The leaders of the three countries said they were "left with no choice" because Iran is no longer "meeting its commitments".
Tehran said its recent move on uranium enrichment was a "remedial step" in line with the deal and that it could be reversed. Iran thinks it can achieve nuclear weapons.
The move makes it more hard to keep the agreement alive.
"The possibility of implementing a dispute mechanism is indeed provided for in the JCPOA [nuclear deal]".
It's been on life support since President Donald Trump unilaterally pulled the United States out in 2018, triggering sanctions that have hurt Iran's moribund economy.
Time and time again, we have expressed our serious concerns to Iran, and urged it to come back into compliance.
Russia's Foreign Ministry said activating the mechanism could make it impossible to resume implementation of the deal.
Iran has gradually been rolling back its commitment after President Trump pulled the US out of the deal in 2018 - and recently announced that it would no longer respect limits set on how many centrifuges it can use to enrich uranium. "Our hope is to bring Iran back into full compliance with its commitments under the JCPoA", they said. "The transparency of Iran's nuclear activities is a key element of the entire nuclear deal", the Foreign Ministry emphasised.
In response, Iran has rolled back its commitments in stages to try and pressure the other countries involved to provide economic incentives to offset the American sanctions, but efforts from them so far have been insufficient.
The Iranian lawmaker elaborated that the betrayals of Western countries to diplomacy, especially after martyrdom of Lt. Gen. Soleimani, by taking a neutral or dual stance towards Iran to comply with US' policies after Trump's withdrawal from the nuclear deal, has moved the atmosphere towards a point where European countries now have to negotiate only with Iranian military officials.
The European powers said they had taken the step to avoid a crisis over nuclear proliferation being added to an escalating confrontation in the Middle East. "Let's work together to replace the JCPOA and get the Trump deal instead", said Johnson after pointing out that the current deal was made by Trump's predecessor, Barack Obama.
The Joint Comprehensive Plan of Action (JCPOA), commonly known as the Iran nuclear deal, was signed in 2015 with the objective of stopping Iran's nuclear weapons development.
Since withdrawing from the agreement, the United States has imposed several rounds of sanctions on Iranian companies and individuals, and even the country's Islamic Revolution Guards Corps.
Iran says it does not feel bound to comply with aspects of the deal except allowing United Nations inspectors into its sites.