Cameron and Merkel hold 'warm and friendly' EU budget talks
David Cameron and German Chancellor Angela Merkel have held "open, warm and friendly" talks about the controversial EU budget, Downing Street says.
At the end of the hour-long meeting Number 10 said "both parties were at the same end of the spectrum".
Mr Cameron had said the EU budget should be frozen or cut, but Mrs Merkel says an increase is necessary.
Officials said discussions on the issue would continue.
Ahead of the crunch talks between the two leaders, Mrs Merkel said she wanted Britain to remain in the European Union.
She was reacting to a call by UKIP leader Nigel Farage for an "amicable divorce" between Brussels and Britain.
Germany has indicated it is sympathetic to the UK's arguments that the EU needs to cut costs, but says some increase in the long-term budget is necessary.
Speaking at a joint press conference with Mrs Merkel before their talks, Mr Cameron said: "We are both believers that European countries have to live within their means, as does the European Union and I know that we will discuss that issue tonight."
Of the EU budget, he said: "At best it should be a cut, at worst a freeze."
Mr Cameron said: "I believe our membership of the European Union is important and that is the basis on which we will be having our discussions tonight."'Wonderful island'
Before their meeting the two leaders had dinner at Downing Street - a starter of spinach and mushroom tart, followed by venison and then traditional German cake for pudding.
Mrs Merkel said the EU budget would "loom large" in the pair's discussions as Britain and Germany had shared interests as net contributors to the EU - and both had to reach a deal with other countries that "will stand up in the court of public opinion back home".
She added: "We will not complete negotiations tonight but we want to do this in the spirit of partnership and friendship in order to focus our interests."
She refused "to be drawn into discussion" of whether Britain should decide if it wanted to leave the EU as the bloc moved towards closer integration, as recently suggested by Polish European commissioner Janusz Lewandowski.
But speaking earlier in the European Parliament, Mrs Merkel had a direct message for the British people - who she called "the inhabitants of this wonderful island" - telling them: "You won't be happy if you are alone in this world."
She was reacting to a speech by UKIP leader Nigel Farage, who urged her to tell Mr Cameron the time had come for "a simple amicable divorce" as feeling in the UK runs completely against the tide of the greater EU integration being promoted by the German leader.
Mrs Merkel hit back by saying: "I cannot imagine that the UK would not be part of Europe."
"I think it is also good for the UK to be in Europe," the German chancellor said, adding she would do "everything" to keep the UK in the EU "as a good partner".
In less than three weeks EU leaders will gather for a summit at which they will try to work out the next set of long-term spending plans for Brussels.
Speaking in Abu Dhabi, during his three-day visit to the Middle East, Mr Cameron said he would make a "very robust and strong argument" for an arrangement that forced the European Commission to limit its budget.
He said: "They are proposing a completely ludicrous 100 billion euro increase in the European budget.'Better deal'
"I'll be arguing for a very tough outcome. I never had very high hopes for a November agreement because you have got 27 different people round the table with 27 different opinions."
Last week the government was defeated in a Commons vote on the EU budget after 53 Conservative MPs defied their party over the issue.
Tory rebels joined with Labour to pass an amendment calling for a real-terms cut in spending between 2014 and 2020.
The amendment was not binding on ministers, but was seen as a blow to David Cameron's authority on Europe ahead of the EU budget summit.
But one of the rebels, Tory MP Douglas Carswell, told BBC News the Commons vote would strengthen the PM's hand, saying: "We might just be able to get a better deal."
Any deal agreed by EU leaders later this month would have to be put to the Commons for approval.
Mr Cameron has said he would be prepared to veto any unacceptable proposal - which would mean that a deal would not go ahead.
If no agreement is reached by the end of next year the 2013 budget will be rolled into 2014 with a 2% rise to account for inflation.