An EU leaders summit backed a "united" approach to keeping Iran deal alive after US President Donald Trump pulled out and reimposed sanctions.
Washington has determined the accord does little or nothing to stop Iran's ballistic missile programme or interference in Middle East conflicts.
"Everyone in the European Union shares the view that the agreement is not perfect, but that we should remain in this agreement and conduct further negotiations with Iran on the basis of other issues such as the ballistic missile programme," Mrs Merkel said.
French President Emmanuel Macron said the bloc was working to keep the existing agreement alive "so that our businesses can remain" in Iran.
"When challenges threaten to destabilise the world, the only solution is to join our forces to respond in one voice. European sovereignty is the guarantor of international stability," he said.
The effort to salvage the Iran deal would run alongside the pursuit of negotiations on a broader agreement.
"The 2015 agreement needs to be completed by a nuclear agreement beyond 2025, an agreement on ballistic activities and (Iran's) regional presence," Mr Macron said.
"International companies with interests in many countries make their own choices according to their own interests," he said. "They should continue to have this freedom.
"But what is important is that companies and especially medium-sized companies which are perhaps less exposed to other markets, American or others, can make this choice freely."
Tehran has warned it is prepared to resume "industrial-scale" uranium enrichment "without any restrictions" unless Europe can provide solid guarantees that it can maintain the economic benefits it gained from the nuclear agreement despite Washington reimposing sanctions.
EU experts have begun work drawing up measures to shield the deal from US sanctions, focusing on nine key issues including ensuring Iran can sell its oil and gas products and have access to international finance.
But given the global reach of US government sanctions it is not clear how effective these measures can be, or whether the EU will try to leverage them as a bargaining chip with Washington.