And she added she was not in favour of pushing for a speedy withdrawal.
Britain narrowly voted to end its membership in a historic referendum last Thursday.
Mrs Merkel was speaking after several EU foreign ministers – including Germany’s – had urged Britain to quickly implement its exit.
“It shouldn’t take forever, that’s right, but I would not fight for a short timeframe,” she said.
She added that she was seeking an “objective, good” climate in the talks with Britain, which “must be conducted properly”.
German Foreign Minister Frank-Walter Steinmeier had earlier said negotiations should begin as “soon as possible”.
He made the comments after an urgent meeting of the six EU founder members to discuss the decision.
British Prime Minister David Cameron has said he will step down by October to allow his successor to conduct talks.
The six countries attending the summit in Berlin – Germany, France, Italy, Belgium, Luxembourg and the Netherlands – first joined forces in the 1950s and still form the core of the EU.
“We say here together, this process should get under way as soon as possible so that we are not left in limbo but rather can concentrate on the future of Europe,” Mr Steinmeier said.
His Dutch counterpart Bert Koenders said the continent could not accept a political vacuum, saying “this will not be business as usual”.
In other developments:
- Scotland’s First Minister Nicola Sturgeon says she will seek “immediate discussions” with Brussels to “protect Scotland’s place in the EU”
- A petition calling for a second referendum on UK’s membership of the EU has gained more than one million signatures
- There are warnings British financial institutions could lose their prized access to the EU if the UK leaves the single market
- Britain’s European Commissioner, Lord Hill, who oversees financial services, is to resign
The first summit of EU leaders with no British representation will be held on Wednesday, a day after Mr Cameron holds talks with members.
Global stock markets and the pound fell heavily on the news of the so-called “Brexit”, while credit rating agency Moody’s cut the UK’s outlook to “negative”.
The UK must now invoke Article 50 of the EU Lisbon Treaty, which sets out a two-year timetable for negotiations on withdrawal.
European Commission head Jean-Claude Juncker said the EU-UK split was “not an amicable divorce”, but nor had they had a “deep love affair”. He has also said exit negotiations should begin immediately.
“Britons decided yesterday [Thursday] that they want to leave the European Union, so it doesn’t make any sense to wait until October to try to negotiate the terms of their departure,” Mr Juncker said in an interview with Germany’s ARD television network.
Leaders of Eurosceptic parties in France, the Netherlands and Italy quickly demanded referendums in their own countries.
“OUTsch!”; “Well done little Britain”; “Completely detached”.
Germany’s press reflects the widespread shock at the British decision to leave the EU. At the highest level of government, no-one really expected this. And they are scrambling to defend German and European interests.
The German position is focused on two major, and delicate, decisions.
Firstly, whether to use Brexit as an opportunity to deepen European integration, or to view it as a “wake-up call” and create more flexibility within the union.
And, secondly, how to deal with Britain – an important trading partner – as a “third country”.
Senior economists and business leaders warn against barriers to free trade.
But politicians are talking tough. Concessions, they say, might encourage other member states to leave. For this reason one senior MP told me: “There must be consequences for Britain”.