David Cameron: I can fix EU 'problem'
David Cameron has said he is "convinced" he can "fix the problems" in the UK's relationship with Europe that the British public find "very frustrating".
Speaking at a press conference with German Chancellor Angela Merkel, the prime minister said he "profoundly" believed the EU needed to be reformed.
Mrs Merkel said she wanted the UK in a "strong and successful Europe".
The two leaders also condemned the deadly shootings in Paris.
They offered their condolences to the French people after 12 people - including journalists and police officers - were killed in an attack on the satirical magazine Charlie Hebdo.
The prime minister was holding talks with the German chancellor in Downing Street, which he said would focus on the global economy, security and the UK's aims for a reformed EU.
Reform, he said, was in the best long-term interests of Britain and Europe.
The prime minister has called for curbs on EU welfare payments ahead of a referendum on Britain's membership of the EU if he wins May's general election.
Commenting on the UK's future in the EU, Mrs Merkel said: "We would very much like to have the UK in a strong and successful Europe."
She insisted there could be "no doubt" about the principle of freedom of movement of people within the EU but accepted there was a need to tackle "abuse" of the rules.
But she declined to comment about whether she would support or oppose any of the changes being sought by Mr Cameron.
The prime minister earlier accompanied Mrs Merkel to an exhibition on the history of Germany at the British Museum.
The five-hour visit, one of a number Mrs Merkel is making to world leaders as part of Germany's year-long presidency of the G7 group of nations, is likely to be her last to the UK before May's general election.
Mr Cameron has called for a far-reaching shake-up of welfare and employment rules across the EU, including requiring migrants to have a job offer before coming to the UK, making them wait four years before they can receive certain benefits and ending the payment of child benefit to dependents of EU migrants overseas.
He has said the proposals will, in some cases, require changes to existing treaties and therefore require the support of all 28 members - most of whom have said they are fundamentally opposed to anything will infringing the principle of the freedom of movement across the EU.
In a joint statement earlier, the two leaders said their talks would focus on tackling instability in the global economy and securing long-term growth, including the prospect of a trade deal between the EU and US.
Analysis by political correspondent Ben Wright
It's a question few voters fret about but it looms over today's talks between David Cameron and Angela Merkel.
The prime minister has said many times he wants Britain to have a renegotiated relationship with the EU embedded in a new Treaty. That deal would then be put to British voters in a referendum before the end of 2017 - if the Conservatives win the coming general election.
But while Germany backs David Cameron on several areas of EU reform - such as limiting the benefits migrants can claim and completing the single market - Berlin does not want a major rewrite of existing treaties now.
It would mean referendums in countries like France and Ireland which may be very hard to win at a time when public confidence in the EU project is fragile.
Some of Mr Cameron's most Eurosceptic backbenchers say a serious, meaningful renegotiation can only be achieved through a new Treaty. Others, like those in the Fresh Start group of Tory MPs, have suggested a reform package they say can be achieved within the existing Treaties.
Berlin is rather miffed David Cameron is already talking about the need for a new Treaty before his proposal has been put on the negotiating table. Either way, the prime minister's plans hinge on having the support of Europe's most powerful leader - which is why his talks with Chancellor Merkel matter.
David McAllister, a member of Mrs Merkel's governing CDU party, said Mr Cameron and Mrs Merkel shared the same views on a wide range of issues central to the EU's future, including growth, competitiveness, financial stability and free trade.
"There is a lot of common ground between Germany and Britain when it comes to the EU and I think we will find a reasonable and decent solution for the British proposals but let's see what actually happens in 2015," he told BBC Radio 4's Today programme.
Labour has complained the Foreign Office did not inform it of Mrs Merkel's visit, although the party stressed leader Ed Miliband had discussed European issues and Labour's EU agenda with the German leader when she last visited the UK in February 2014.
"The Foreign Office usually contacts the Leader of the Opposition's office in advance of visits from heads of government and state. Unfortunately on this occasion they failed to do so," a Labour spokesman said.
It is understood that Mrs Merkel did not ask to meet Mr Miliband during her visit to the UK.
Labour, which supports fresh curbs on benefits for migrants but does not support a referendum unless additional powers are handed to Brussels, said there was an "unbridgeable gap" between what Tory MPs wanted and what Germany would accept.