The European Union on Monday called for talks to avert escalation as Britain issued a stark warning about the risk of conflict erupting "by accident" in the Persian Gulf amid rising tensions.
The EU’s diplomatic chief Federica Mogherini stressed the need for dialogue as "the only and the best way to address differences and avoid escalation" in the region.
She made the comments ahead of a regular EU foreign ministers' gathering in Brussels.
US Secretary of State Mike Pompeo arrived in the Belgian capital on Monday to discuss the Iran nuclear deal on the sidelines of the meeting with his counterparts from Britain, France and Germany – the three European signatories to the 2015 accord that curbed Iran's nuclear program in return for sanctions relief.
After Brussels, Pompeo will head to the Russian Black Sea resort of Sochi on Tuesday to meet President Vladimir Putin and Foreign Minister Sergei Lavrov, a State Department official said.
Mogherini gave a chilly response to news of Pompeo's visit, which she said was only communicated to Brussels at the last minute.
"We'll be here all day with a busy agenda so we'll see during the day how and if we manage to arrange a meeting," she told reporters.
"We continue to fully support the nuclear deal with Iran, its full implementation," Mogherini said.
"It has been and continues to be for us a key element of the non-proliferation architecture both globally and in the region."
Iran last week announced it was suspending some of its commitments under the agreement, a year after US President Donald Trump withdrew from the accord and reimposed sanctions on the Islamic Republic – putting the deal in peril.
Iranian President Hassan Rouhani issued an ultimatum to the Europeans on Wednesday, threatening that Iran would go further if they fail to deliver sanctions relief to counterbalance Trump's renewed assault on the Iranian economy within 60 days.
The EU is trying to implement a new channel to allow Iran to sell its oil and circumvent newly-instated US sanctions, but setting it up is proving complex.
The US has sent an amphibious assault ship and a Patriot missile battery to the Persian Gulf, having already deployed an aircraft carrier and B-52 bombers.
British Foreign Secretary Jeremy Hunt called for "a period of calm" as he arrived for talks in Brussels.
“What we need is a period of calm, so that everyone understands what the other side is thinking,” he said.
"We are very worried about the risk of a conflict happening by accident with an escalation that is unintended on either side but ends with some kind of conflict," Hunt said.
"This is already the most unstable region in the world and it would be a massive step in the wrong direction."
Hunt added, “We'll be sharing those concerns with my European counterparts, with Mike Pompeo.”
French Foreign Minister Jean-Yves Le Drian joined the criticism of the US, saying Washington's move to step up sanctions against Iran "does not suit us."
German Foreign Minister Heiko Maas said the Iran agreement is “necessary for our security.”
"That is why we will continue to support the implementation of this agreement," he added.