President Trump and President Macron spoke to the media at the end of the G7 summit (Picture: PA).
US President Donald Trump said he would be open to a meeting with Iranian officials if "the circumstances are correct".
French President Emmanuel Macron said he hopes a meeting could be arranged in the "coming weeks" between the US President and his Iranian counterpart.
Speaking at the end of the G7 Summit in France, Mr Macron said the surprise invitation of Iran's foreign minister offered a "road map" to end escalating tensions between the US and Iran.
Standing alongside Mr Macron, Mr Trump said: "At a given point in time there will have to be a meeting between the American and Iranian president."
Mr Trump also said there was a "really good chance" of a meeting happening.
On Sunday, Iran's Foreign Minister made an unscheduled visit to the summit in Biarritz but did not meet Mr Trump.
Mohammad Javad Zarif was invited by Mr Macron in an effort to ease tensions between the two countries.
Mr Trump said he gave his approval for the invitation, despite new US sanctions against the envoy.
In a televised speech, Iran's President Hassan Rouhani said: "If I knew that going to a meeting and visiting a person would help my country's development and resolve the problems of the people, I would not miss it.
"Even if the odds of success are not 90% but are 20% or 10%, we must move ahead with it. We should not miss opportunities."
In a public address on Tuesday, Mr Rouhani was quoted as saying the United States needs to make the first step towards dialogue by lifting sanctions against Iran.
Tensions between the US and Iran have been rising since Mr Trump pulled the US out of the 2015 Iran nuclear deal - a move opposed by Mr Macron and other G7 leaders.
The US has since imposed new sanctions and deployed additional military assets to the Gulf region, amid the tensions.
The UK, Australia and Bahrain have all joined a US-led maritime security mission to protect international shipping vessels travelling through the region.
Tensions over Iran, Russia, the US trade war with China and the faltering global economy dominated the three-day summit.