David Cameron has warned the EU must be "flexible and imaginative enough" to respond to demands for reform, as he visited Paris on his whirlwind diplomatic tour.
Addressing the media alongside French President Francois Hollande, the Prime Minister said the status quo was "not good enough".
But he expressed confidence that solutions could be found to make Europe more competitive and "address the concerns of the British people" ahead of an in-out referendum on membership.
After Mr Hollande stressed France wanted the UK to remain in the EU and signalled that he was ready to look at "suitable" proposals for change, Mr Cameron said: "My priority is to reform the European Union to make it more competitive, and to address the concerns of the British people about our membership.
"The status quo is not good enough. I believe there are changes we can make that will not just benefit Britain, but the rest of Europe too.
"Of course the priority for Francois is to strengthen the eurozone to ensure a successful single currency, and Britain supports that.
"We want to help the eurozone work better and we do not want to stand in the way of closer integration. So we have different priorities but we share one objective, which is to find solutions to these problems.
"What matters is that the EU and its 28 members are flexible and imaginative enough to respond to these issues and to work together to find answers that will make the EU more successful.
"That is the challenge of our times and I believe strongly that we can meet it."
Earlier the Prime Minister met Dutch counterpart Mark Rutte for a working lunch in The Hague, as he bids to remould the relationship with Brussels.
After dining with Mr Hollande, he will head for Warsaw for talks with Polish counterpart Ewa Kopacz tomorrow and then Berlin to see Chancellor Angela Merkel - whose backing is crucial to success.
A visit to Copenhagen to meet Danish premier Helle Thorning-Schmidt was cancelled after she called a snap general election.
The whistle-stop tour came as Foreign Secretary Philip Hammond said "substantial" reforms were needed for the Government successfully to recommend staying in the EU.
"The Prime Minister is very clear in dealing with European counterparts that if we are not able to deliver on these big areas of concern that the British people have, we will not win the referendum when it comes," he told BBC Radio 4's Today programme.
"We expect our European Union partners to engage with us in delivering a package that will enable the British people to decide that Britain's future is best delivered inside the European Union.
"We expect that some of our partners will adopt a hard line at the start of the negotiations - that's how negotiation works - but we are very confident that, over the course of the summer and perhaps onwards through the winter, we will be able to negotiate a substantial package of reform which will address the concerns that the British people have."
Mr Hammond confirmed that the Government believed the reforms it was seeking - particularly on curbing migrants' access to benefits - would require changes to the EU treaties, potentially making it harder to get an agreement.
"The advice that we are getting is that we will need treaty change in order to underpin particularly the changes on migration and welfare benefits. That is the best legal advice that we are receiving," he said.
Under the provisions of the EU Referendum Bill, tabled in Parliament today, the referendum - which will determine whether the UK remains a member of the EU - has to be held before the end of 2017.
While Mr Hammond confirmed the Government had not ruled out the possibility that it could take place next year, he sought to play down the prospects of an early vote.
"I would urge people not to speculate on an early date. We are absolutely clear that we have to get this right. We are certainly not going to trade substantive reform just for getting it done quickly. We have to get it done properly," he said.
The Referendum Bill also sets out the wording of the referendum question, with voters being asked if the UK should "remain a member" of the European Union when they go to the polls.
It means supporters of Britain retaining its ties to Brussels will form the Yes campaign when the vote comes.
The Conservatives' previously-preferred wording - ''Do you think that the United Kingdom should be a member of the European Union?'' - has been dropped following concerns by the Electoral Commission that some people might think the country was not already a member.
Instead the watchdog's recommended question - "Should the United Kingdom remain a member of the European Union?" - has been adopted.
Chris Grayling, the new Commons Leader, has announced that the second reading of the EU Referendum Bill will take place on Tuesday June 9.