The president wants Congress to modify a law that reviews US participation in the nuclear deal to include "trigger points" that, if violated, would lead to the United States reimposing its sanctions, the official said.
"The proper implementation of the agreement should be accompanied by a strengthened dialogue with Iran on its ballistic program and its regional policy, in order to guarantee better stability in the Middle East", the French presidency said in a statement on the call.
Regarding the U.S.'s continued involvement in the Iran nuclear deal - which Trump has called multiple times "one of the worst deals I've ever seen" - the president said: "Despite my strong inclination, I have not yet withdrawn the United States from the Iran nuclear deal".
The deal saw Iran agree to reduce uranium enrichment activity drastically, dispose of its enriched uranium stocks and modify a heavy water facility so it could not produce material suitable for a nuclear bomb.
The Trump administration asked Congress then to come up with and pass a companion agreement that addresses those issues.
Iran has insisted they have complied with the deal, with Zarif tweeting that the EU is "fully aware" of the country's compliance.
"The United States will not stand by while the Iranian regime continues to engage in human rights abuses and injustice". Work already has begun on this front, the official said.
German Foreign Minister Sigmar Gabriel said since Iran is abiding by the deal, there is no reason to reconsider sanctions.
Iranians walk past a Ghadr-F missile displayed at a Revolutionary Guard hardware exhibition, marking 36th anniversary of the outset of Iran-Iraq war, at Baharestan Sq.in downtown Tehran, Iran, September 25, 2016.
Many of the foreign ministers in Western Europe are concerned that Donald Trump will pull the US out of the 2015 Nuclear Deal today and hurt the people who will overthrow the Iranian Regime.
In accordance with a mechanism set up by Congress, the nuclear agreement has to be re-assessed by an American president every 90 days.
The waiver he will sign suspends US sanctions on Iran for 120 more days.
But Trump paired Friday's concession with other, targeted sanctions on Iran for human rights abuses and ballistic missile development.
European countries including France and Italy have benefited from renewed trade with Iran, whose proven natural gas reserves are as vast as Russia's, while Britain reopened its embassy in Tehran following the deal.