Trump has called the existing accord "insane" and "ridiculous", in part because its restrictions start to expire in 2025.
But addressing the US Congress at the end of his pomp-filled, 3-day visit to Washington, French President Emmanuel Macron said: "Iran shall never possess any nuclear weapons. Not now. Not in 5 years. Not in 10 years. Never."
He has proposed an additional deal that extends Iran's nuclear restrictions while also curbing its ballistic missile program and support for militias in the Middle East.
In Iran, Rouhani took a more aggressive tack, reiterating that the Islamic republic would not accept any changes to the deal.
"We have an agreement called the JCPOA," said Rouhani in a fiery speech, using its technical name.
"It will either last or not. If the JCPOA stays, it stays in full."
From Europe, a host of voices have urged Trump to build on the deal, rather than tear it up.
"There is one deal existing, it's working, it needs to be preserved," said EU diplomatic chief Federica Mogherini.
Moscow also reiterated its support, with Kremlin spokesman Dmitry Peskov telling reporters: "We believe that no alternative exists so far" to the nuclear deal, and demanding that Iran be involved in any further discussions.
The next to press the point will be German Chancellor Angela Merkel when she visits Washington on Friday, April 27.
"The biggest priority is maintaining the existing nuclear accord. It was negotiated by 7 countries and the EU and can't be renegotiated by one or other party," said German foreign spokesman Rainer Breul.
"President Macron... spoke of the need for supplementary agreements. The question is whether, and in what circumstances, Iran would be ready to enter into such a process," he added.
'A high-rise builder'
Rouhani's speech was particularly fiery, ridiculing Trump as "a trader, a businessman, a high-rise builder, how can he judge about global issues?
"You have no expertise in politics, nor in law, nor in international accords," he said.
Iran has the support of all other parties to the accord, who say it is working and Tehran has stuck to its commitments.
Macron, who has built a warm rapport with Trump, has positioned himself as an emissary for European officials seeking a compromise that allows the mercurial US president to claim a public victory, while keeping the deal intact.
But for now, even Macron had to admit he could not read whether Trump would simply walk away from the existing deal when the renewal deadline arrives on May 12.
True to his background in reality TV, Trump has kept everyone guessing.
"This is a deal with decayed foundations," he said. "We're going to see what happens on the 12th."
Iran has warned it will ramp up enrichment if Trump scraps the accord, prompting a blunt warning from the US leader.
"They're not going to be restarting anything. If they restart it, they're going to have big problems, bigger than they ever had before. And you can mark it down," Trump said.
The proposal that Macron put forward to his US counterpart involves preserving the existing agreement on the first of "4 pillars" of a future deal.
The others would address the period after 2025, when certain clauses concerning nuclear activities will sunset; Tehran's highly controversial ballistic missile program; and its "destabilizing" role in the region.
"For me it's progress, it avoids falling into the complete unknown if the US decision is a hard exit," said Macron, who confirmed that the proposal was a strategy coordinated with European partners and not a unilateral one.
Some hawkish American officials argue that the Europeans, particularly Germany, oppose a tougher stance against Iran to safeguard their business interests there.
That is sharply rejected by European officials, who are increasingly frustrated at spending time handling Trump's complaints rather than focusing on the deepening crises of the Middle East.
The disagreement threatens to plunge transatlantic relations to their lowest point since the Iraq war, despite the lavish welcome Trump put on for Macron's state visit.
And meanwhile, Western countries have found themselves increasingly sidelined from issues such as the Syrian war – underlined again on Wednesday when Iran, Russia and Turkey announced a new summit to discuss the conflict this Saturday, April 28, in Moscow. – Rappler.com