Top European diplomats on Saturday called on Britain not to delay its exit from the European Union, saying that negotiations must start as soon as possible, while acknowledging wider dissatisfaction among EU citizens.

Britain must invoke Article 50 of the Lisbon Treaty "as soon as possible" in order to trigger Brexit talks, German Foreign Minister Frank-Walter Steinmeier said after meeting counterparts from France, Italy and the Benelux countries - the founding members of the EU.

However, in a joint declaration released after the meeting, the six foreign ministers also expressed their regret over Britain's decision to leave the EU and said they would continue their efforts "to work for a stronger and more cohesive European Union of 27 based on common values and the rule of law."

At the same time, it was important to acknowledge "different levels of ambition" among its members regarding the integration process and to ensure that Europe would better "meet the expectations of all European citizens," they said.

"We are aware that discontent with the functioning of the EU as it is today is manifest in parts of our societies. We take this very seriously and are determined to make the EU work better for all our citizens," the declaration adds.

Once Article 50 is activated, Britain has two years to negotiate the terms of its withdrawal.

Britain should not "play a game of cat-and-mouse" by delaying negotiations on leaving the 60-year-old bloc, which would prolong market uncertainty in the EU's already battered economy, Luxembourg Foreign Minister Jean Asselborn said.

French Foreign Minister Jean-Marc Ayrault added that Cameron must step down and be replaced "in the coming days," despite the British leader's announcement on Friday that the succession would only be decided in time for his Conservatives' party conference in October.

The meeting - which took place in the Villa Borsig, the Foreign Ministry's guest house - was hosted by Steinmeier to discuss next steps and to consult on an EU reform initiative that would allow more resistent members to carve out a looser relationship to Brussels.

Initiated by Germany and France, the reform effort is intended to prevent countries with strong eurosceptic movements such as France and the Netherlands from holding votes similar to Britain's in-out referendum, in which 52 per cent voted to leave.

"We must be given the opportunity to show that Europe is necessary, but also able to act" on issues including management of the refugee crisis and youth unemployment, Steinmeier said after the meeting.

West Germany, France, Italy, Belgium, the Netherlands and Luxembourg established the European Economic Community in 1957, the forerunner for today's EU.

Saturday's meeting faced criticism from those who argue that any attempt at reform should involve all 27 remaining member states.

Steinmeier responded by saying there would be "many different conversations" about Britain's exit in the coming days.

"We must now listen to each other and get a feel for the expectations and whether there is room for manoeuvre," he said.

German Vice Chancellor Sigmar Gabriel, also the leader of the Social Democrats, meanwhile said it should not be impossible for Britain to return into the EU fold, as the Brexit referendum did not represent the will of all British citizens.

"Almost three quarters of those aged below 25 wanted to stay inside the EU. We mustn't pull up the drawbridge," Gabriel told the papers of the Funke group in comments to be published on Sunday.

Merkel is hosting EU President Donald Tusk, Italian Prime Minister Matteo Renzi and French President Francois Hollande in Berlin on Monday, the eve of a two-day EU leaders summit in Brussels.

Didier Seeuws, a senior Belgian diplomat and member of the EU Council of Ministers, has been named the EU's chief negotiator for the British exit from the bloc.

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