Outraged by the result of the British vote, the bloc's leaders have multiplied calls for London to leave the European Union swiftly.
Britain's planned departure was "not an amicable divorce" said European Commission chief Jean-Claude Juncker, stressing that it should be quick.
Foreign Minister Frank-Walter Steinmeier and his French counterpart Jean-Marc Ayrault also joinly called for ambitious steps to strengthen the European Union.
But in the heated cacophony, the leader of Europe's biggest economy made a strong call for calm.
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Speaking today, she said Europe could "not afford to have a long period of uncertainty" which would "not be good for either the EU's 27 member states or Britain".
But she said it was understandable that London needed time.
"I also understand that Britain needs a certain period of time to analyse the situation."
While Britain considers its options, the German leader also insisted no backroom deals be done before London triggers Article 50 to formally start the process of leaving the bloc.
Britain's notification will set the clock ticking on a two-year period of negotiations within which a basic withdrawal agreement should be made.
After that "the treaties shall cease to apply to the state in question" - or in layman's terms, Brexit will become a reality, unless all the parties unanimously agree to extend the talks.
German conservative daily Die Welt said that taking time to reflect is Merkel's signature approach.
"Be it in the euro or in the refugee crisis, Germany has always sought to buy time, in order to solve problems," it said. "Now in the Brexit crisis, she has given Cameron this time."
"Indeed, that would miss the real lesson of the Brexit vote. European politicians instead need to find a solution to the demands of the public - and they need to realise that European citizens want 'less Brussels' and not more," it added.
But some saw Merkel's position as a sign of dithering and weakness.