"We have therefore been left with no choice, given Iran's actions, but to register today our concerns that Iran is not meeting its commitments", the foreign ministers of the three countries wrote in a letter.
The Europeans may be trying to salvage the deal with the step, but could end up hastening its demise and risk an Iranian backlash that could end the extensive IAEA monitoring and verification of Iran's nuclear program, several analysts said they feared.
"Of course, if the Europeans. seek to abuse [this process] they must also be prepared to accept the consequences", Iran's foreign ministry said in a statement.
Under the mechanism, if the party accused of failing to live up to its commitments does not resolve the complaint against it, the party or parties that triggered the mechanism can cease their own commitments to the JCPOA, notify the UN Security Council, or both.
A propaganda video circulating in Iran dramatizes the assassination of President Donald Trump, Secretary of State Mike Pompeo, and Israeli prime minister Benjamin Netanyahu.
European Union foreign policy chief Josep Borrell, who coordinates the agreement on behalf of the world powers, said the pressure on Iran from Europe does not mean worldwide sanctions will automatically be slapped on the Islamic Republic.
The strategic aim for the United Kingdom, and our global partners, remains as it has always been: to de-escalate tensions, to hold Iran to account for its nefarious activities, and to keep the diplomatic door open for the regime to negotiate a peaceful way forwards.
Britain's prime minister is calling for it to be scrapped and replaced with a new, quote, "Trump deal". "Our hope is to bring Iran back into full compliance with its commitments under the JCPoA".
"Let's work together to replace the JCPOA with the Trump deal", he told the BBC.
Iran rolled back on its uranium enrichment constraints detailed in the worldwide agreement earlier this month after one of its top military commanders, Qassem Soleimani, was assassinated in an American drone strike in Iraq.
However, they added that putting Iran on notice did not mean they were joining Washington in applying maximum economic pressure on Tehran.
The European powers said they were acting to avoid a crisis over nuclear proliferation adding to an escalating confrontation in the Middle East. Russia, another signatory to the pact, said it saw no grounds to trigger the mechanism and Iran dismissed the step as a "strategic mistake".
His comment "let's dial this down" coming as Trump assumed a boastful and aggressive stance towards Iran, has been seen as an attempt to mock the United States president.
It comes as Iran announced it would refuse to comply with any of the restrictions the JCPOA had placed on the country's nuclear programme. "The transparency of Iran's nuclear activities is a key element of the entire nuclear deal", the Foreign Ministry emphasised.
Foreign Secretary Dominic Raab told the House of Commons the DRM was being triggered because Iran had "undermined" the objective and goal of the JCPOA.
We urge Iran to work with us to save the deal.