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Macron said he wanted to see the original deal preserved but also called for further talks on areas the Trump administration has singled out for criticism, including "the control of nuclear activity beyond 2025," according to the statement.
A readout of the call provided by the Iranian government included an accusation from Rouhani that the US had breached the agreement by criticizing it ahead of President Donald Trump's decision about whether to abandon the deal.
The "current conduct of the United States would be in breach of the JCPOA," Rouhani said, referring to the Joint Comprehensive Plan of Action.
He said that the Trump administration's negative comments about the deal had created "fear and ambiguity for different countries and businesses for their relations with Iran," possibly damaging the country's economy.
Rouhani said that even if the deal remained in place despite Trump's objections, it would no longer be acceptable to Tehran if matters continue "the way it has been going in the past two years."
However, he had also told Macron the deal is "not negotiable," according to the Iranian statement.
"The EU, including France, supports the nuclear agreement and we will stay in the nuclear agreement 100%," Rouhani said.
Complications arise
Macron's conversation with Rouhani followed a flurry of diplomatic activity over the weekend, as the leaders of the United Kingdom and Germany joined their French counterpart in attempting to bolster the original 2015 accord.
Following calls with Macron, both Germany's Angela Merkel and the UK's Theresa May agreed an emphasis had to be placed on preventing Iran from obtaining a nuclear weapon.
"They [the three leaders] agreed that there were important elements that the deal does not cover, but which we need to address -- including ballistic missiles, what happens when the deal expires, and Iran's destabilizing regional activity," a statement from the UK government said.
On Sunday, newly appointed US Secretary of State Mike Pompeo, again reasserted opposition to the deal in it current form, calling Iran "the greatest sponsor of terrorism in the world."
"We are determined to make sure it never possesses a nuclear weapon. The Iran deal in its current form does not provide that assurance," said Pompeo, during a visit to Saudi Arabia.
"We will continue to work with our European allies to fix that deal. But if a deal cannot be reached, the [US] President has said that he will leave that deal," he added.
Pompeo had previously said it was "unlikely" Trump would agree to keep the deal.
Macron's series of high-level calls follow his trip to Washington last week, where he attempted to personally convince Trump to stay in the Iran deal.
Iranian Foreign Minister Mohammad Javad Zarif said on April 23 it was "either all or nothing."