Publicly, EU capitals still support the 2015 Iran deal as the best mechanism to keep Tehran's nuclear ambitions in check while easing the sanctions that have crippled its oil-dependent economy.

But as President Trump doubles down on his rejection of the accord and threatens more sanctions, and Tehran responds by threatening to resume some nuclear activity, diplomats are pessimistic.

This week one European official in Brussels admitted to AFP that hopes of saving the deal are getting "weaker and weaker", after the latest EU-US diplomatic encounter laid bare the growing rift.

"No negotiation is possible with the US administration on Iran, on climate, on the Nord Stream 2 pipeline, because President Trump refuses to change his positions," one diplomat said.

This came after EU commissioner Miguel Arias Canete and US energy secretary Rick Perry failed to paper over their many differences at an uncomfortable press briefing.

With the White House bent on confrontation, the only hope of saving the Iran deal-implementation mechanism, the Joint Comprehensive Plan of Action or JCPOA, lies with Tehran.

If Iran's Islamist government continues to honour its side of the accord, Europe will continue to seek ways to deepen economic ties.

But efforts to set up a "special vehicle" to facilitate trade without exposing EU companies to US sanctions have yet to enable a single transaction, and Europe is losing credibility.

Iran now warns it will restart heavy water production and some nuclear enrichment in 60 days if the Europeans, Russia and China are not able to offset the damage of renewed US sanctions.

"For the moment, Iran's announcements are not a violation of nor an exit from the nuclear deal," one senior EU official told AFP, "but the situation is extremely worrying."

On Thursday, Paris, Berlin, London and EU foreign policy chief Federica Mogherini issued a statement rejecting Iran's "ultimatum", but announcing no immediate new action of their own.

Instead they appear to be awaiting a report at the end of May by the IAEA nuclear watchdog on whether or not Iran is in breach of its JCPOA promise to rein it its nuclear programme.

"We don't impose sanctions on the basis of announcements, but the Iranians know perfectly well what they risk if they cross the line," the senior EU official warned.

That line is not yet crossed.

Iran currently holds 124 tonnes of heavy water, and is permitted 130 under the JCPOA. It has 163.8 kilos of enriched uranium, less than the deal's 202.8 kilo ceiling, according to the IAEA.

Iran has also agreed not to enrich this uranium above the level of 3.67 percent, so if international inspectors are correct, it is still far from the threshold for making a weapon.

Nevertheless, Iranian President Hassan Rouhani's announcement dismayed the Europeans as a needlessly provocative tactic, even if there is some sympathy for his domestic plight.

- 'Viable economy' -

"Rouhani is in a very difficult position for economic reasons," a European diplomat told AFP.

Rouhani, who is not Iran's ultimate ruler but serves under Supreme Leader Ali Khamenei, must demonstrate to regime hardliners that he is not standing idle while the accord unravels.

So he was frustrated by what Tehran sees as the Europeans' failure to react when Trump put an end to waivers that allowed some countries to import Iranian crude without facing US sanctions.

Iranian oil exports, which stood at around 1.5 million barrels per day last year, have fallen to 700,000, according to an EU source who warned this is "insufficient to maintain a viable economy".

But even if Europe wanted to help, it is not a big enough client.

European imports from Iran amounted to only 10 billion dollars in 2017, nine billion of that in energy supplies. Iran imported 10 billion in EU products.

"The European Union never promised that it could itself compensate for the effect of US sanctions," an EU official said. "For oil, Iran needs to look to its main clients, India and China."

And what of Europe's special vehicle, now known as INSTEX?

This was set up by France, Germany and Britain to serve as a payment mechanism to allow Iran to trade with Europe without passing through US-controlled commerce in dollars.

Iran is furious that the mechanism has yet to be put to use, but Europe insists that the fault lies with Tehran -- saying the Islamic republic has failed to set up a mirror-entity to control its side of trades.