Defending the deal today at the European University Institute's state of the union conference, Mogherini said it had opened up trade while providing security in the region.
The administration says the lifting of sanctions as part of the nuclear pact had allowed Iran to build up its military, with Trump claiming on Saturday that Tehran's defense spending had risen by 40 percent since 2015.
So far, China, France, Russia, Britain, the European Union and Iran remain in the accord, which placed controls on Iran's nuclear program and led to a relaxation of US economic sanctions against Iran and companies doing business there.
And Germany said it will spend the next few months trying to persuade Washington to change its mind. "It depends on the conduct of other governments".
"The PM said the United Kingdom would continue to work with the USA to keep up the pressure on North Korea to denuclearise".
President Donald Trump's announcement last Tuesday that the USA was exiting the 2015 nuclear accord was met with widespread dismay in Europe where companies now face the threat of sanctions if they do business with Iran.
German Chancellor Angela Merkel, as quoted by local media, accused the United States of undermining the global order by its decision to exit the UN Security Council-endorsed Joint Comprehensive Plan of Action (JCPOA) that governs Iran's nuclear program.
President Trump's decision to pull out of the nuclear deal and Iran's missile exchanges with Israel are just ramping up the pressure in a country that's already dangerously close to boiling point. But in an interview aired on the ABC's This Week program, Bolton said, "That's not the policy of the administration".
"Iran was likely to respond with tougher, more defiant policies to President Donald Trump's announcement on Tuesday that he was pulling the United States out of the JCPOA", Schirach said.
"We could have pushed the Europeans a lot harder, to work with us", Gates said on "Face the Nation".
The two leaders agreed for their teams to hold discussions on the potential impact of U.S. sanctions on firms doing business in Iran.
He said: "I think, just speaking for the United States, the President has chose to leave the deal".
"I think at the moment there's some feeling in Europe - they're really surprised we got out of it, really surprised at the reimposition of strict sanctions".
Bolton said Europe was still digesting Trump's May 8 move.