This was UK PM Theresa May's first overseas trip
German Chancellor Angela Merkel has warned against a period of limbo before Article 50 is activated, to allow Britain to leave the EU.
Mrs Merkel stressed that the UK must formally announce its intention to leave the EU before Brexit talks can begin.
However, she added that the "close bonds of partnership and friendship" between Germany and the UK remain intact despite the vote to leave the European Union.
Mrs Merkel said it was in everyone's interest for the UK to have a clear view on the type of relationship it wants with the trading bloc before Article 50 is invoked and formal Brexit talks commence.
During a joint news conference in Berlin, British Prime Minister Theresa May confirmed her government was taking time to determine its objectives before the two years of negotiations is triggered - and this will not be before the end of 2016.
In response, the German Chancellor warned no one wants a period of limbo before Article 50 is activated.
Mrs May stressed that she wanted the UK's departure to be orderly and constructive, and expressed hope that the country would secure the "closest relationship" with Germany after Brexit.
She said she believed the referendum result was an indication that Britons wanted greater control over immigration, while retaining a good trade deal with Europe.
Mrs May told reporters that she defined "sustainable" levels of net migration as in the tens of thousands - considerably less than the hundreds of thousands of people currently coming to the UK each year.
This is her first overseas trip as the UK prime minister.
The pair are set to have a working dinner on Wednesday night, with Mrs May travelling on to Paris to meet French President Francois Hollande on Thursday.
In addition to discussing the EU, Mrs May and Mr Hollande are expected to discuss cooperating on counter-terrorism measures in the wake of last week's terror attack in Nice.