Boris Johnson insisted Brexit will not see the UK "abandon its leading role" in Europe as the UK's new Foreign Secretary made his debut on the international stage.
Arriving for his first meeting of the EU's Foreign Affairs Council, Mr Johnson also called on the Turkish government to show "restraint" after the crackdown following the attempted military coup.
Mr Johnson said he had had a productive 45-minute meeting with EU foreign affairs chief Federica Mogherini on Sunday and was looking forward to presenting a positive case for Brexit.
He said: "It's very, very good to be here for my first overseas trip.
"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 we are leaving Europe. We are not going to be in any way abandoning our leading role in European participation and co-operation of all kinds.
"I had a very good conversation to that effect with High Representative Mogherini and she very much agreed that is a role Britain should continue to play.
"When you look at the discussion on the table this morning over the horrific events in Nice, and Turkey where we have to work very closely together, you see the importance of that.
"On Nice, we will be ensuring that we co-ordinate our response to terror.
"On Turkey, it is very important in light of the failed coup that we see restraint and moderation on all sides, and that is what I will be calling for.
"In the meantime, I am very much looking forward to meeting my colleagues from other European countries."
Mr Johnson, whose RAF aircraft had to be diverted to Luton Airport en route to Brussels, after technical problems, is expected to face turbulence on the ground at the summit as other EU countries seek answers on the UK's "divorce deal" stance, which is expected to be raised on the margins of the gathering.
As British Prime Minister Theresa's May's surprise choice to head Britain's post-Brexit diplomatic efforts, Mr Johnson is in the international spotlight as never before.
US Secretary of State John Kerry was holding breakfast talks with Mr Johnson and the other EU foreign ministers as the situation in Turkey and the aftermath of the Nice atrocity drew attention away from Brexit.
But the issue of EU migrants rights triggered debate again as Brexit Minister David Davis warned that any surge in immigrants before Britain formally leaves the EU could lead to new curbs.
Mr Davis, who is in charge of exit arrangements, insisted that a cut-off point may need to be imposed on when newcomers to the country gain full residency rights if the UK's impending withdrawal sees migrant numbers increase.
The foreign ministers' summit came as Mrs May was visiting Wales, which joined England in voting for Brexit, to underline her commitment to withdrawal, and the embattled steel industry.
Mrs May was meeting First Minister Carwyn Jones at the Welsh Assembly in Cardiff and reaffirming that she will "fully engage" with the Welsh Government on Brexit negotiations.
The visit was taking place as leaders from the North of England demanded a place at the Brexit negotiating table with the PM.
Ms Mogherini sidestepped questions about whether it would be "awkward" dealing with Mr Johnson after he compared the EU's ambitions to those of Hitler during the referendum campaign, saying that the two had a "very positive exchange" at their meeting.
The EU foreign affairs chief said Mr Johnson would be welcomed "as a new member of the family".
But Ms Mogherini stressed negotiations could not start on Brexit details until London formally triggered withdrawal under Article 50 of the Lisbon Treaty.
"There are no negotiations before the notification of Article 50 is tabled. Until that negotiation comes to an end, the UK is a full member of the EU so our common work on foreign and security policy continues," she said.
French foreign minister Jean-Marc Ayrault said he has already had "frank" exchanges with Mr Johnson as he urged early negotiations.
"I had a telephone conversation with him on Saturday. This exchange was frank, but useful. I think it is important that we, together, work for the future of relations between the EU and Britain.
"Regarding France, we always have exceptional bilateral relations with Britain that we want to continue, especially in defence, immigration... economically and in particular the nuclear issue.
"There is much to do with Britain. I always speak to Boris Johnson with the greatest sense of sincerity and frankness. This is how we must move forward, and in the case of France with a purpose: to prevent Europe moving into a situation of uncertainty as regards the future of relations with Britain. So the earlier negotiations begin, the better," he said.