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During a trip to Berlin, May said she and German leader Angela Merkel had reaffirmed their commitment to Iran's nuclear deal and the need for full implementation.
"And we agreed that as we continue to work to preserve the deal we also share the US concerns about Iran's destabilising activity in the Middle East, and we stand ready to take further appropriate measures to tackle these issues," May told reporters.
British foreign minister Boris Johnson said on Monday that London was concerned at Iran's role after anti-aircraft fire on Saturday downed an Israeli warplane returning from a bombing raid on Iran-backed positions.