"The Presidents of Russia and France spoke in favour of keeping the Plan and its strict observance," the Kremlin said, referring to the Joint Comprehensive Plan of Action.
The statement was released after Macron called Putin to inform him of his talks with Trump in the United States.
Trump faces a May 12 deadline to decide on the fate of the Iran nuclear accord and is demanding changes that European capitals believe would represent a legal breach.
On Sunday, US National Security Advisor John Bolton said the mercurial US president had not yet decided whether to scrap the accord.
Macron, who held talks with Trump last week, has positioned himself as an emissary for European officials seeking a compromise that would keep the deal intact.
Macron has earlier proposed an additional deal that extends Iran's nuclear restrictions.
Russia has said that there was "no alternative" to the agreement and that Iran's position was on the issue was paramount.
Iran's President Hassan Rouhani rejected any hopes of rewriting the nuclear deal.