At the end of a mini-summit with German Chancellor Angela Merkel and French President François Hollande, Mr Renzi said improved security and intelligence sharing is an “absolute priority” for a Europe confronting Islamic extremist violence.
Mr Hollande stressed in particular the need for common European defence efforts after a string of deadly attacks in France and other European countries.
The three leaders held a press conference aboard the Italian aircraft carrier Garibaldi, which is co-ordinating the EU’s Mediterranean migrant rescue operation, after paying tribute to one of the founding fathers of European unity on the island of Ventotene.
Standing silently together, the trio placed three bouquets of blue and yellow flowers — the colours of the European Union — on the simple white marble tombstone of Altiero Spinelli in the cemetery on Ventotene.
Mr Spinelli, along with another intellectual confined to Ventotene in the 1940s by Italy’s fascist rulers, co-wrote the Ventotene Manifesto, which called for a federation of European states to counter the nationalism that had led Europe to war.
The document is considered the inspiration for European federalism.
Mr Renzi invited his French and German counterparts to Ventotene to remind Europe of its founding ideals as the EU forges ahead after Britain’s vote to leave.
They then moved on to the Garibaldi.
Ahead of the summit, Mr Renzi wrote of the venues: “Two symbols in one: idealistic values and concrete commitment.
“We want that the Europe after Brexit — the Europe hit in its heart by terrorism — will relaunch the powerful ideals of unity and peace, freedom and dreams, dialogue and identity.”
For Ms Merkel, the visit to Ventotene marked the start of a string of meetings with other EU leaders to discuss the post-Brexit EU. She will be in Estonia, the Czech Republic and Poland in the coming days.
Ms Merkel has also invited leaders from the Nordic countries, Holland, Austria and other eastern European nations for informal meetings at a government guest house in Germany.
“She wants to support a discussion that is as broad as possible, with as many actors involved as possible,” her spokesman, Steffen Seibert, said last week.
That is aimed at ensuring that whatever emerges from the post-Brexit process “finds the widest possible acceptance in the member states and in the population”.