Angela Merkel at centre stage of bid to ensure EU unity after Brexit

She signalled that she is taking the initiative, inviting her counterparts from France and Italy - the two other largest remaining members - to meet her on Monday in Berlin as well as EU President Donald Tusk.

But, true to a methodical approach to problems tried and tested over a decade in power, she also sought to slam the brakes on any hasty decisions, arguing that the 27 remaining members must avoid drawing "quick and simple conclusions" that would only create further divisions.

Germany has traditionally been reluctant to exert an overt leadership role in Europe, though it has been increasingly assertive in recent years in designing the response to the eurozone's debt troubles and, less conclusively, in seeking an EU-wide response to the influx of refugees and other migrants from the Middle East and elsewhere.

Even now, with one of the EU's heavyweights on the way out, Berlin is not likely to seek a sole leadership role, ever conscious of the historical burden of its Nazi past.

"It will continue to lead with and through groups," said Daniela Schwarzer, an expert on EU affairs at the German Marshall Fund of the United States think-tank in Berlin.

"There's this really strong concern to always be part of something and not going it alone.

"Germany has a huge interest that the Brussels institutions have more support than they currently have," she added, and there is no sign that it "actively seeks power and a hegemonic position".

Guntram Wolff, director of the Bruegel think-tank in Brussels, said Brexit will mean can no longer be addressed by shifting coalitions of France, the UK and Germany.

Instead, it would increase the dependency between France and Germany - the traditional motor powering EU integration, but one that has sputtered somewhat over recent years amid differences on the debt crisis and other issues.

"In that couple, Germany is the stronger player, quite clearly," he said. "So in that sense it will probably increase the role of Germany in the EU."

German officials left open what exactly the response to the British referendum might be. Finance minister Wolfgang Schaeuble said earlier this month that "we couldn't simply call for more integration" if Britain leaves.

The remaining 27 EU members should "calmly analyse and evaluate the situation and, on this basis, together make the right decisions," Ms Merkel has said.

She acknowledged that people all over the continent increasingly have doubts about the direction of the European unification process, and added: "We must ensure that citizens can feel in concrete terms how much the European Union contributes to improving their personal situation."

Foreign minister Frank-Walter Steinmeier said leaders should focus on finding "common European solutions where they are missing" - for example, to the migrant crisis, and doing more to boost jobs and growth.

Mr Steinmeier said the bloc should fall neither into hysteria nor shock, and must acknowledge that it does not yet have answers to all the questions raised by the British referendum result.

On Saturday, he hosted his counterparts from the EU's other five founding members and said there will need to be further discussions "in big formats and in smaller formats".

With Britain's departure, Germany will lose a traditional ally within the EU on matters such as free trade and competition. Britain was the number three destination for German exports last year and was Germany's fifth-biggest trading partner overall.

"Germany on many economic issues relies more on the UK and Poland than it traditionally relies on France, because they have a more similar mindset on those issues," Ms Schwarzer said.

Ms Merkel sounded a notably conciliatory note towards Britain in responding to the referendum, signalling what appears to be "a willingness to lower the cost of Brexit for both sides", she added.

"Our aim should be to shape future relations between Great Britain and the European Union so that they are close and based on partnership," Ms Merkel said. She said she wants an "objective, good" climate in talks on Britain's exit and there is "no need to be particularly nasty in any way in the negotiations".

Germany will also be losing a fellow major contributor to the EU budget.

The leader of the upstart nationalist Alternative for Germany party, which has risen in polls during the migrant crisis at the expense of Ms Merkel's and other parties, raised that issue. Celebrating what she called "a signal to the Brussels politburo and its bureaucratic appendages", Frauke Petry said the government should not simply "plug the British net contribution with German tax money".