Macron has been leading efforts to de-escalate the situation and he expressed hopes of bringing together Rouhani and Trump for a meeting during a G7 summit days ago.
But Rouhani has downplayed the likelihood of that happening unless the United States first lifts crippling sanctions that it has slapped on Iran
since pulling out of the deal.
"If Europe cannot operationalise its commitments, Iran will take its third step to reduce its JCPOA commitments," Rouhani reportedly told Macron in the phone call.
However, "this step, just like the other ones, will be reversible," he added, quoted on the Iranian government's website.
"Unfortunately after this unilateral move by the US, European countries did not take concrete measures to implement their commitments," he continued.
"The contents of JCPOA are unchangeable and all parties must be committed to its contents," he said.
Rouhani said Iran had two priorities: for all parties to the JCPOA to fully implement their obligations and "securing the safety of all free maritime transportation in all waterways including the Persian Gulf and Strait of Hormuz".
Macron's office released a statement later Saturday in which he stressed the importance of "the current dynamic to create the conditions for a de-escalation through dialogue and building a durable solution in the region." A French diplomatic source said it was important, after recent discussions between Paris and Tehran, to establish that President Rouhani was "still ready to negotiate. And that is the case." Twelve months on from the US pulling out of the nuclear deal, Iran began reducing its commitments.
The UN's nuclear watchdog, the International
Atomic Energy Agency, said Friday that just over 10 percent of Iran's uranium stockpile was now enriched up to 4.5 percent, above the 3.67 percent limit stipulated in the 2015 deal.
It also said Iran's total stockpile of uranium, which under the accord should be no more than the equivalent of 300 kilograms (661 pounds) of uranium hexafluoride, now stood at roughly 360 kilograms.
Iran has not specified what its third step might be in reducing its commitments to the deal.
Foreign Minister Mohammad Javad Zarif said in a recent interview with the Sueddeutsche Zeitung newspaper that the step would be taken on September 6.