After Macron said he hoped to arrange such a meeting in the "coming weeks," Trump said, "If the circumstances were correct or right, I would certainly agree with that."
"In the meantime, they have to be good players," Trump said. Otherwise, he said, Iran will be met with “violent force.”
Macron said Rouhani was open to a meeting with Trump as well. The two presidents spoke over the weekend after Macron met with Iran's Foreign Minister Mohammad Javad Zarif on the sidelines of the G-7 summit.
Asked by ABC News Chief White House Correspondent Jonathan Karl if it sounds realistic to organize a meeting with Iran within just a matter of weeks, Trump said "it does."
"I think he's going to want to meet. I think Iran wants to get this situation straightened out. Is that based on fact or based on gut? That's based on gut," Trump said. "But they want to get this situation straightened out, Jonathan. They're really hurting badly."
Macron invited Zarif to the G-7 summit over the weekend as he and other European leaders try to mediate between the U.S. and Iran amid high tensions in the Persian Gulf. France, Germany, and the United Kingdom remain in the Iran nuclear deal, but after Trump withdrew from the pact and reimposed intense U.S. sanctions, Iran has lashed out and seized or attacked oil vessels.
“I hope that in the next few weeks based on our discussions, we will be able to achieve the meeting that I just mentioned between President Rouhani and President Trump. Myself and the partners who have a role to play in nuclear negotiations will also be fully involved in these negotiations,” Macron said.
While the president expressed openness to the idea, Trump sounded nonchalant about whether the diplomatic effort, with France as a mediator of sorts, ultimately pans out.
“Maybe it works, maybe it doesn't. I say it all the time about everything. Maybe it works and maybe it doesn't,” he said.
But in a possible change of position, Trump seemed to drop the long list of demands that his Secretary of State Mike Pompeo had once made of Iran.
"We're looking for no nuclear weapons, no ballistic missiles and a longer period of time. Very simple," Trump said Monday, compared to a May 2018 speech by Pompeo where he listed 12 demands for a new deal with Iran. That included ending support for the Houthi rebels in Yemen and terror groups like Hezbollah and Hamas, withdrawing its forces from Syria, and no longer threatening Israel.
While Trump may be open to talks, it's unclear whether Iran is, too. Supreme Leader Ayatollah Khamenei has previously rejected the idea, calling Trump untrustworthy and insincere, but the country's president Rouhani indicated some openness on Monday after his phone call with Macron, but before Trump spoke.
"I would not hesitate attending a meeting and meeting someone if I know our people's problems are solved. What matters the most is our national interests,” Rouhani said, according to Iran’s Fararu News.
Trump and Macron also papered over what seemed like a rift over the visit of Iran’s foreign minister Zarif to the G-7. Trump allies like Sen. Lindsey Graham, R-South Carolina, said it was "terribly disrespectful," but Trump insisted that he was not blindsided by the meeting and supported it.
“President Macron told me exactly what was happening, who was coming, what time they were coming, where they were going to meet,” the president said, although he said it was "too soon" for him to meet Zarif, who his administration sanctioned last month and blasted as a propaganda minister.
Macron, asked whether he asked for Trump's permission before meeting with Zarif or if he informed the president of the meeting, made clear that he informed the president.
“I informed President Trump that it was my idea, not to involve the United States, not to say this is on behalf of you, of everybody, but to say as friends I think it would be a good idea to ask him to go back and try to negotiate something. So I did it on my own, I informed -- before making it, President Trump was informed,” Macron said.
Macron was also asked whether he has concerns about Trump’s trade war with China hurting the global economy. He said, "What’s bad for the world economy is uncertainty and the quicker an agreement is arrived at, the quicker that uncertainty will dissipate.”
ABC News's Somayeh Malekian contributed to this report from Tehran.