During the phone call, the German chancellor said that the discussion on details of the agreement should continue.
During a visit to Europe this week President Hassan Rouhani warned that Iran could reduce its co-operation with the United Nations nuclear watchdog, having already threatened Trump of the "consequences" of fresh sanctions against Iranian oil sales.
The Iranian president said there was no action plan or "a clear method in the proposed package for the continuation of cooperation and, similar to the previous European Union statements, it only contained general commitments".
"Maintaining access to these markets is a quasi life-or-death issue for the [bank]" because it has $120 billion of bonds held by investors worldwide that must be continually rolled over and refinanced, Director-General Bertrand de Mazieres said in May.
Speaking at a joint press conference with his Swiss counterpart, Alain Berset, in Bern on Tuesday, Iranian President Hassan Rouhani lashed out at American officials for threatening to stop Iran's oil exports, saying they would never be able to carry out such a threat.
Foreign ministers from Britain, China, France, Germany and Russian Federation will meet their Iranian counterpart in Vienna on Friday for the first time since the U.S., an original signatory to the 2015 pact, pulled out of the deal.
A senior USA military leader said in 2012 the Guards have the ability to block the Strait of Hormuz "for a period of time" but the United States would take action to reopen it in such an event.
A top U.S. official says on Jul 2 that Washington is determined to force Iran to change behaviour by cutting its oil exports to zero, confident the world has enough spare oil capacity to cope.
But Britain, France and Germany say they are determined to save the deal and its economic benefits for Iran.
Washington has since told countries they must stop buying the OPEC producer's oil from November or face financial consequences.
It is unsurprising that the USA is using this as an excuse to issue a bunch of new statements about their military commitment, and is liable to be an excuse for more United States naval operations along the Iranian coast. Further sanctions on oil and transactions with the central bank of Iran will come into effect November 6.
"If the process of the European foreign ministers' meeting in Vienna, which is aimed at encouraging Iran to cooperate, is promising, we will continue our cooperation", he said.
In light of Washington's push on sanctions, European leaders have said they would do their utmost of maintain business ties with Iran but it would be hard for them to make any "guarantees".
Now, the threat of USA sanctions has increasingly darkened the outlook for Iran's economy, helping to stoke a plunge in the Iranian rial this year that has driven up prices and provoked street protests and strikes.
The Iranian president said, "After the U.S. unilateral and illegal exit, Moscow has an important role in the reinforcement of the JCPOA and fulfillment of the opposite sides' commitments".