Here is a look at what may be in the works, and the challenges a new deal could entail.

- Macron's proposal -

In a press conference at the White House, Macron said the 2015 Iran nuclear deal did not go far enough, while crediting it for allowing the international community "some control" over Iran's nuclear activities.

Other areas still need addressing, he said, namely: Iran's nuclear activities after 2025 when so-called sunset clauses in the current deal kick in; Iran's ballistic missile activities; and a political means to limit Iran's activities in Yemen, Syria, Iraq, and Lebanon.

Iran is a key ally of Syrian President Bashar al-Assad, supports Hezbollah militias in Lebanon and backs Yemen's Huthi rebels, who are locked in a war with a Saudi-led coalition.

"It's not about tearing apart an agreement and having nothing, but it's about building something new that will cover all of our concerns," Macron said.

The French president said France and its allies want "sustainable stability," following months of Trump anger at the original Iran deal and threats to back out of it.

"I believe that the discussions we've had together make it possible to ... pave the way for a new agreement, an agreement on which we will work, and beyond our European partners, we would like to involve the regional powers, and of course, Russia and Turkey," he said.

Macron indicated his suggestion was for a separate accord that would run alongside the current deal.

"I'm not saying that we move from one agreement to another," he said.

The proposal appears to repackage a solution previously floated by the Europeans to meet Trump's demands, by taking a tougher line on Iranian missile activity and Tehran's regional influence, but without ripping up the existing nuclear deal.

- What's at stake -

With a hollowed-out State Department, even a transatlantic deal could prove an epic undertaking for the Trump administration, and Iran has already signalled that any talk of curbing its missile program is off limits.

Further, Trump has shown little appetite for international deal-making.

The existing nuclear deal was struck in 2015 after 21 months of grueling diplomacy.

In return for the lifting of punishing international sanctions, Iran froze its nuclear program, ending a 12-year standoff with the West, which worried it was developing a nuclear bomb.

Britain, China, France, Russia, the United States and Germany signed off on the deal that, among other things, requires Iran to slash the amount of uranium it can enrich.

- Trump's view -

Trump has continually lambasted the accord signed by his predecessor Barack Obama, calling it at one point the "worst deal ever."

On Tuesday, he described it as "insane," and in October he refused to certify that Iran was respecting its commitments on the pact -- though he stopped short of walking away altogether.

At least on first blush, the US leader appeared receptive to trying to reach some sort of grand bargain.

"I think we will have a great shot at doing a much bigger, maybe, deal," said Trump, stressing that any new accord would have to be built on "solid foundations."

"They should have made a deal that covered Yemen, that covered Syria, that covered other parts of the Middle East," said Trump.

The next decision deadline for Trump on the Iran deal is May 12.

"We're going to see what happens," he said.