"We are always committed to improving security and stability in the region and will work toward this goal," Rouhani was quoted as saying by his website.
Macron's phone conversation was part of a French initiative to prevent an escalation of tensions in the Middle East, Reuters reported, citing a statement issued by Macron's office.
The increased friction between Tehran and Washington has raised fears of a military conflict in the region, according to Financial Tribune.
Relations between the two old foes further deteriorated after US President Donald Trump pulled his country out of a 2015 nuclear deal, formally known as the Joint Comprehensive Plan of Action, last year and reimposed harsh sanctions on Iran.
The situation has worsened in recent months, especially following Iran's downing of an American drone in its southern skies last week, which the US retaliated by imposing new sanctions after calling off a planned strike on Iranian targets.
Rouhani noted that the US drone was shot down after it violated Iranian airspace and after several warnings from Iran.
"If the Americans want to violate the waters or airspace of Iran again, Iran’s armed forces have a duty to confront them decisively," he said.
Reversible Measure
Rouhani said if JCPOA had been implemented completely and correctly by all sides of the negotiations, positive developments would have occurred in the region and the world.
"Conditions [with Washington] will not change, unless the US lifts all sanctions against Iran," he said.
Tehran's continued adherence to the deal, according to Rouhani, was based on the European parties' promises to safeguard the country's interests by facilitating banking relations and oil exports, but "unfortunately none of them has been fulfilled".
"If Iran cannot enjoy the benefits of JCPOA, it will reduce its commitments step by step as per articles 26 and 36 of the deal," he said.
Iran already stopped its compliance with two of the JCPOA obligations on May 8 and is to further reduce them on July 8, after a 60-day deadline, if Europeans take no action.
The president, however, noted that Iran would never take an irreversible measure and will return to its full commitments once the remaining parties guarantee the country's banking ties and oil export.
Rouhani also stressed that under no circumstances will Iran renegotiate a deal that was reached after two years of talks.
"By imposing and tightening sanctions against the Iranian people …, the Americans have proved that they are by no means willing to address the issues."
The French president expressed regret over the US exit from JCPOA and its reimposition of sanctions, reiterating France's commitment to preserve the deal by reconciling both sides, especially the US.
Macron also called for a collective effort to prevent provocative moves in the Persian Gulf.