BRUSSELS (Reuters) - New Foreign Secretary Boris Johnson said he would assure his EU counterparts on Monday that Britain would continue to cooperate closely with them once it leaves the bloc following last month's Brexit referendum.

"The message I'll be taking to our friends in the council is that we have to give effect to the will of the people and leave the European Union but that in no sense means that we are leaving Europe," the Brexit campaigner told reporters on arrival at an EU foreign ministers meeting in Brussels.

"We are not going to be in any way abandoning our leading role in European cooperation and participation of all kinds," added Johnson, a former Brussels-baiting journalist who was on his first foreign trip since being appointed in a surprise move last week by new Prime Minister Theresa May.

Johnson had on Sunday met EU foreign policy chief Federica Mogherini, with both stressing their meeting had been held in good spirits, discussing a joint response to the failed coup in Turkey and the militant attack in Nice.

"On Turkey, I think it's very important in view of the failed coup that we see restraint and moderation on all sides and that's what I'll be calling for," Johnson said.

Asked how ministers would find working with Johnson, who during the Brexit campaign compared the EU to Hitler's plan to dominate Europe, Mogherini simply said her exchange with him on Sunday evening had been "very positive".

She stressed that Britain remained a member of the European Union and that there would be no negotiation of the terms of Brexit until London notifies formally that it is leaving under the terms of Article 50 of the EU treaty.

(Reporting by Alastair Macdonald; Editing by Robert-Jan Bartunek)