Defending the global institutions Trump has consistently attacked, Macron called for the U.S. to join France in revitalizing the foundations they built together across the 20th century: "We can build the 21st century world order based on a new breed multilateralism, based on a more effective, accountable and results-oriented multilateralism".
The host also said that, when she served under President George W. Bush, she never saw any leaders conduct themselves so differently with regard to their foreign counterparts within a single visit.
But any desire Trump had for the French proposal - and the close relationship he has established with Macron - didn't appear to overcome his steadfast opposition to the existing agreement.
An eloquent if hard-nosed pragmatist, Macron says he pressed Trump to accept that the deal, while imperfect, was better than no deal, and that it could be strengthened to speak to Trump's concerns.
In his speech, Macron advocated multilateralism, which his USA counterpart Donald Trump has not been quite a fan.
Trump described his war of words a year ago with Kim as "very, nery nasty", but stood by his approach. One possibility is an idea, long under consideration, to seek to negotiate a successor to the JCPOA with Iran.
As such, the Europeans may claim that they are willing to impose sanctions on Iran for missiles that can reach Israel, but he noted that the "truth is, they are not willing to impose any sanctions that are meaningful for those missiles".
They shook hands, held hands and clasped hands, The Washington Post reported.
Yesterday Presidents Macron and Trump called for a new deal with Iran - after President Trump again called the current arrangement "insane". "Not now, not in five years, not in 10 years, never".
Diplomats have cited progress on ballistic missiles and on inspections, but the "sunsets" issue remained unresolved.
Avengers: Infinity War's Iron Spider Suit Is In Marvel's Spider-Man
Director Jon Watts is returning to helm the Spider-Man sequel along with the first films writers Chris McKenna and Erik Sommers. In Marvel's Spider-Man, having a variety of suits for players to use was a must-have for us.
"The United States is the one who invented this multilateralism", he went on.
But he warned against abandoning the multi-nation Iran nuclear deal, which has been publicly considered by Mr Trump.
In Geneva, a U.S. nonproliferation official, Christopher Ford, laid out such an approach without providing details.
"We are not discussing renegotiating the agreement - that is not what the two presidents were talking about", Mogherini told reporters after an global conference on Syria. "We are seeking a supplemental agreement that would in some fashion layer upon it a series of additional rules". "Since 2015, the USA and Europe have not hit a single one of those entities for non-nuclear reasons. With what right?" Mr Rouhani said in a speech, reported AFP.
Macron tried to counter suggestions of dissent among the Europeans. "We'll see also if I do what some people expect, whether or not it will be possible to do a new deal with solid foundations".
Dalibor Rohac, a research fellow at the American Enterprise Institute, said he is skeptical that anything will happen before May 12 to change Trump's mind, even with the added European pressure of a White House visit Friday by German Chancellor Angela Merkel.
In Iran, Rouhani responded by ridiculing Trump, saying: "You have no expertise in politics, nor in law, nor in worldwide accords".
"For what? With what right?" he added.
The deal agreed with Tehran and six global powers restricts Iran's nuclear program in exchange for relief on economic sanctions against the country. "Therefore, distinguished members of the Congress, let us put them aside, write our own history and a future we want".
"How can he pass judgements on global affairs?"
Mr Rouhani accused Mr Trump of lacking in experience.