David Cameron has rebuffed criticism at home and abroad of his commitment to hold a referendum on the UK's future in Europe if he wins the next election.
Labour and the Lib Dems have said plans to renegotiate the UK's membership and put it to a public vote was a gamble and against the national interest.
France and Germany warned the UK against pursuing an "a la carte" approach. The US said the UK and the EU were stronger together.
But the PM said he had public backing.
And he said Labour's arguments were "fatally undermined" by confusion over their own position.
Mr Cameron's promise to give the British people "their say" on Europe - in the form of an in/out referendum to be held before 2018 - has been welcomed by most Conservative MPs and eurosceptics in other parties.
MPs will get the opportunity to debate the plan in the House of Commons next Wednesday.
At the next election - expected in 2015 - the Conservative leader said his party would offer people a "simple choice" between staying in the EU under new terms, or leaving the 27-member union altogether.
'Destiny'
He said the issue of the UK's future in Europe would not "go away" and now was the right time to confront it when the EU was set to go through a period of profound change amid calls for further integration.
In a long-awaited speech, Mr Cameron said the referendum would be a decision on the UK's "destiny" and, if he secured a new relationship he was happy with, he would campaign "heart and soul" to stay within the EU.
While he believed the UK could survive outside the EU, he said withdrawal would be a "one-way ticket" and he appealed for "cool heads" in the debate to come.
The prime minister rejected suggestions that a new relationship was "impossible to achieve" and dismissed calls for the referendum to be held sooner, saying such a "momentous decision" must wait until the UK's relationship with the EU "had been put right".
"Our approach is what the British people want. It is right for business, right for the economy and we will fight for it in the years ahead."
However, Mr Cameron did not spell out what powers he would like to see the UK take back as part of a new settlement or what would happen if the negotiations did not go his way.
'Wriggle room'
The Conservative leader has been under pressure from many of his MPs to give a binding commitment to a vote on Europe.
But Foreign Secretary William Hague told the BBC that Mr Cameron's message was not "confined or directed" to his backbenchers or those voters attracted by the UK Independence Party's call for EU withdrawal and should resonate across Europe
"It is not the Conservative Party he is speaking to. It is the British public and the European public."
Conservative MPs who want a looser relationship with the EU welcomed Mr Cameron's promise and said it had united the party.
One MP, Mark Reckless, even suggested Mr Cameron had left his own position in a referendum "up for grabs" and had the "wriggle room" to campaign for an exit if he believed this was the only option left for Britain.
Labour said Mr Cameron was "going to put Britain through years of uncertainty, and take a huge gamble with our economy".
But their leader Ed Miliband came under pressure himself after he appeared to go further than he has done before and told MPs that he opposed the idea of an in/out referendum.
The opposition have previously declined to rule out a referendum in the future while arguing that now is not the right time for one, but party sources insisted their position had not changed.
'Ill-defined'
Lib Dem leader Nick Clegg, who is also deputy prime minister, said there was a "right place and right time" for a referendum.
But he added: "My view is that years and years of uncertainty because of a protracted, ill-defined renegotiation of our place in Europe is not in the national interest because it hits growth and jobs."
The UK Independence Party said the "genie was out of the bottle" about a possible exit from the EU but acknowledged that winning a referendum on a platform for withdrawal would not be easy.
Conservatives have said their reform message is likely to win favour with European allies such as Sweden and the Netherlands.
German Chancellor Angela Merkel said she would listen to British "wishes" but her foreign minister Guido Westerwelle said "cherry picking is not an option" before adding that Europe needed more, not less, integration.
And French foreign minister Laurent Fabius warned: "You can't do Europe a la carte... to take an example which our British friends will understand - imagine Europe is a football club and you join, once you're in it you can't say 'Let's play rugby'".
President Obama's press secretary, Jay Carney said he welcomed Mr Cameron's call for Britain to remain in the European Union, adding: "We believe that the United Kingdom is stronger as a result of its European Union membership and we believe the European Union is stronger as a result of having the United Kingdom in the EU."
No 10 said the British public would have the final say.
Q&A
What has happened?
Prime Minister David Cameron has delivered a speech (full text) setting out his views on the UK's future in the European Union. The speech has been months in the planning.
Why the big deal about the speech?
Mr Cameron had been facing mounting pressure from within the Eurosceptic ranks of his own Conservative Party, and the UK Independence Party, who are unhappy with the current relationship between the UK and the European Union. There have been calls for a referendum to be held, and his own MPs want to see action on the Conservative election pledge to "bring back" powers to Westminster from Brussels. For months now, the promise has been that these questions will all be answered in a big speech.
So what did Cameron say?
Mr Cameron said he plans to renegotiate parts of the UK's relations with Europe and put that changed membership package to the British people in an in-out referendum after the next general election, by the end of 2017. That, obviously, also depends on the Conservatives winning a majority in 2015. To see more of what he said, here are selection of key extracts from the speech.
What sorts of powers does the UK want back?
The prime minister did not spell this out in his speech, but there is a cross-government audit currently under way looking at where the EU has powers over life in the UK. The idea is that each one will then be examined to see whether it is necessary or whether the power could be "brought back" to the UK. Areas it might include are the Working Time Directive, which imposes employment rules such as limiting the working week and giving EU workers a minimum number of holidays each year. The UK is also keen on opt-outs from policing and criminal justice measures. The 2010 Conservative manifesto said: "We will work to bring back key powers over legal rights, criminal justice and social and employment legislation to the UK."
Why does Cameron think he can agree changes with EU leaders?
The recent eurozone crisis has led those countries using the single currency to believe that they need closer integration in future - a move which will further increase the gap between the euro and non-euro EU members. Mr Cameron says there needs to be a new EU treaty to facilitate the eurozone integration, so, as part of negotiations, there is a chance to redefine the membership rules for countries like the UK.
So does this all mean that the UK's going to leave the EU?
David Cameron said that he opposed the idea of the UK leaving the EU (the UK joined when it was the European Economic Community, in 1973). However he did say during a recent BBC radio interview: "Would Britain collapse if we left the European Union? No, of course not. You could choose a different path. The question is, what is in our national interest? I've always been very clear it's in our national interest as a trading nation to be in the single market."
What has been the reaction in the UK?
Eurosceptics seem seem pretty happy with the speech - it has been very warmly welcomed by Conservative MPs. Although the UK Independence Party said it wanted a referendum sooner, party leader Nigel Farage called the PM's promise of an in/out referendum his party's greatest achievement.
Pro-Europeans have been unhappy with the speech - Deputy Prime Minister Nick Clegg warned that proposing a referendum at a future date causes uncertainty and will have a "chilling effect" on jobs and growth. Ex-European Commissioner and Labour cabinet minister Lord Mandelson called it "game, set and match" to the hardliners in Mr Cameron's party.
The BBC has compiled a selection of responses to the speech.
What about the reaction around Europe?
The BBC's Steve Evans in Berlin said opinion was hardening in Germany and France, with many politicians believing that those opposed to further European integration would be better off "leaving gracefully". Guido Westerwelle, German foreign minister, said "cherry picking is not an option". French foreign minister Laurent Fabius said: "We want the British to be able to bring all their positive characteristics to Europe... but you can't do Europe a la carte. I'll take an example which our British friends will understand. Let's imagine Europe is a football club and you join, but once you're in it you can't say, 'Let's play rugby'." Read more EU reaction.
What about the reaction from business?
A succession of business leaders have spoken up in favour of UK membership of the EU and the US and a range of European politicians have also warned of negative results if the UK left the EU. Some business leaders, such as IG Group founder Stuart Wheeler and Next boss Lord Wolfson, have also called for changes in the UK's relationship with the EU. The director general of the employers' group the CBI, John Cridland, said "closer union of the eurozone is not for us" but Mr Cameron "rightly recognises the benefits of retaining membership of what must be a reformed EU".
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