Iranian President Ebrahim Raisi said on Monday that any talks about Iran's nuclear programme must ensure his country's "rights".
In an hour-long phone call with Mr Raisi, French President Emmanuel Macron urged Tehran to resume negotiations quickly.
Mr Raisi told Mr Macron that Iran was serious about "maintaining deterrence" in Gulf waters, after accusations from Israel and its allies, mainly the US, that it was behind a deadly tanker attack off Oman.
It was the ultra-conservative president's first reported call with a western leader since taking office last week.
He took over from Hassan Rouhani, a moderate under whose two-term presidency the 2015 nuclear agreement was signed.
It provided international sanctions relief in exchange for limits on Tehran's nuclear programme.
Former US president Donald Trump three years later withdrew Washington from it and reimposed crushing sanctions.
"In any negotiation, the rights of the Iranian people must be upheld and the interests of our nation ensured," Mr Raisi told Mr Macron, the Iranian presidency's website said.
Mr Macron "called on Iran to quickly resume negotiations in Vienna to reach a conclusion and to put an end, without delay, to all nuclear activities that violate the  agreement", the French presidency said.
In response to the reimposed sanctions, Iran pulled back from most of its main nuclear commitments under the deal.
Six rounds of nuclear talks between Iran and world powers were held in the Austrian capital between April and June to try to revive the accord.
The last round concluded on June 20, with no date set for another.
Iranian officials had said negotiations would not resume before the new government took over, while an EU official said at the weekend that meetings could resume in Vienna from early September.
The accord's remaining parties are Britain, China, France, Germany and Russia.
"The Americans clearly violated their obligations by imposing new sanctions," Mr Raisi told Mr Macron.
He also spoke of the "failure" of European members to the deal to help Iran circumvent US sanctions.
The two leaders also stressed the need to strengthen bilateral relations, their offices said.
During his swearing-in ceremony on Thursday, Mr Raisi repeated Iran's official position that it was pursuing only "peaceful" nuclear technology, and said he would support "any diplomatic plans" to lift the sanctions.
But "the policy of pressure and sanctions will not cause the nation of Iran to back down from following up on its legal rights", he said.
Iran has recently also faced warnings and accusations from Israel and its allies over a deadly tanker attack, for which it denies responsibility.
The MT Mercer Street, an oil products tanker operated by Israeli-controlled Zodiac Maritime, was struck on July 29 off Oman's coast. Two crew members, a Briton and a Romanian, were killed.
Iran has warned Israel not to take military action against it after its arch-foe threatened Tehran over the tanker attack.
"The Islamic republic is very serious about providing security and maintaining deterrence in the Persian Gulf and Sea of Oman Region," Mr Raisi told Mr Macron, without referring directly to the incident or accusations.
Iran "will confront elements that deprive the region of its security", he said.
US Secretary of State Antony Blinken also renewed vows on Monday to hold Iran accountable for the tanker attack, saying the world cannot allow "impunity".
"Failing to do so will only fuel their sense of impunity and embolden others inclined to disregard the maritime order," Mr Blinken told an online Security Council session on maritime security.