Federica Mogherini, who is also the EU’s foreign affairs chief, said Brussels had both the ‘hard’ and ‘soft’ power needed to accomplish the task.
Speaking at the Lennard Meri Conference, Estonia, she said: “There is a European way to security that is never purely and only military.
“You take any crisis or security threat in the world of today, and you realise that the hard power, the military means are always necessary but never enough.
“The European Union has this unique mix of hard power that needs to be increased because it’s not enough, what we have now, but we have at the same time the soft power.
“And this unique mix if we manage to increase our hard power, position ourselves in a place that can be very helpful for our partners in the world to tackle some security issues.”
Ms Mogherini said if the bloc had the “political courage” to take on the role, it could become an institution that provides worldwide security.
She continued: “The world is complex and there is not one single instrument that will make it.
“So I think that the work we have ahead of us is huge but we have, if we are self-confident and we take the political courage to use the potential we have, we could be indeed the security provider for European regions, and more largely the world, needs in partnership.”
Ms Mogherini said: “We underestimate the power we have, and underestimating or downplaying it we hurt ourselves. I think the main challenge Europeans have, when it comes to their role in the world, is a lack of self-confidence.
“You ask me if it is still possible to have a foreign policy without the UK? Sure, I think the UK will face many more problems than us after the Brexit.
“The very same fact that it has taken them more than nine months to start negotiations after the results of the referendum tells you it is much more complicated than they calculated.”
Last month a former UK ambassador to NATO said that crumbling security across Europe means the continent is closer to war than it has been in decades.
Sir Adam Thomson, who is now Director of the European Leadership Network, said the risk of an armed conflict breaking out was at the highest point in decades, as tensions between Nato and Russia are rising, as well nationalism and populism coming to the fore across European nations.
He said: “Security right across Europe is eroding right now, I would say war is a higher risk than it has been in decades. That’s Ukraine, but also the western Balkans, it’s the Nato-Russia confrontation, it is rising populism and nationalism.”
Sir Adam added the UK leaving the EU would not necessarily have a larger impact on the alliance unless the negotiations turned sour.
He added: “It doesn’t necessarily damage Nato at all, the greatest damage to Nato would be if the security relationships erode and worsened because of… Brexit.
“The security relationship for post-Brexit Britain with the EU is too important, it’s not so much a card to be played in Brexit negotiations as an area to be protected from the more toxic areas of the negotiation.”