Mr Macron, on a three-day visit to the US, is the first foreign leader to be treated to a state visit during the Trump presidency.

"We do have a very special relationship," Mr Trump told journalists gathered in the Oval Office.

But whether or not the French president felt humiliated by the bout of unexpected grooming, he did manage to get Mr Trump's attention on the Iran nuclear accord.

He framed his appeal to preserve the deal with the promise of a "bigger, better" one.

In other words, build on the existing agreement to address its flaws, rather than scrap it and start fresh.

Whether or not this is possible is an open question.

But the suggestion was enough to intrigue Mr Trump.

His tone changed, moving from a blistering harangue of the deal before the meeting to something more considered - although still noncommittal - afterwards.

And that shows the influence of personal engagement with the president, from someone who - like Mr Macron - knows how to talk to him.

What was Iran's response?

On Monday, Iranian President Hassan Rouhani threatened "severe consequences" if the US withdrew from the deal.

President Macron and his wife, Brigitte, attended a state dinner in their honour at the White House on Tuesday - the first of Mr Trump's presidency.

Guests included former Secretary of State Henry Kissinger and Apple chief executive Tim Cook.

The Iran deal is not the only potential source of discord between the two leaders.

Also on the agenda is the Paris climate accord, the US decision to recognise Jerusalem as the capital of Israel, and planned US tariffs on EU steel and aluminium.

Mr Trump earlier thanked France for joining the US and Britain earlier this month in launching air strikes after an alleged chemical attack in Syria.