David Cameron has outlined his four goals for reforming the UK's membership of the EU, including restrictions on benefits for people coming to the UK.
He said Britain faced a "huge decision" in the in/out referendum promised before the end of 2017.
But he said he was confident of getting what he wanted from reform talks.
Anti-EU campaigners say the talks are a "gimmick" - and the European Commission said the UK's benefits proposals could break free movement laws.
The changes the UK wants
Mr Cameron formally set out his demands in a letter to the president of the European Council Donald Tusk saying four objectives lie at the heart of the UK's renegotiations:
- Protection of the single market for Britain and other non-euro countries
- Boosting competitiveness by setting a target for the reduction of the "burden" of red tape
- Exempting Britain from "ever-closer union" and bolstering national parliaments
- Restricting EU migrants' access to in-work benefits such as tax credits
Mr Cameron hit back at claims by former Tory chancellor Lord Lawson that the four goals were "disappointingly unambitious", saying they reflected what the British people wanted and would be "good for Britain and good for the European Union".
"It is mission possible and it is going to take a lot of hard work to get there," said the prime minister.
Analysis by BBC Europe Editor Katya Adler
The European Union realises the British prime minister needs a fight and a bloody nose to drown out criticisms back home that this EU reform process is a sham; that Mr Cameron's demands are wishy-washy and worthless.
They realise he needs a sense of drama. Of a bitter battle fought and won. And they are preparing to give it to him.
But there are also some very real difficulties with the changes to the EU that David Cameron demands from a European perspective. Read more from Katya
What Mr Cameron said in his speech
David Cameron said benefit restrictions were needed to cut "very high" and "unsustainable" levels of immigration but added: "I understand how difficult some of these welfare issues are for some member states, and I'm open to different ways of dealing with this issue."
He claimed 40% of recent European Economic Area migrants received an average of around £6,000 a year of in-work benefits - although others have questioned those figures.
The prime minister said he wants the UK to stay in a reformed EU, but he has not ruled out recommending leaving if he cannot secure the change he wants with the leaders of the other 27 EU countries.
He did rule out a second referendum if Britain voted to leave, saying: "You the British people will decide. At that moment you will hold this country's destiny in your hands. This is a huge decision for our country - perhaps the biggest we will make in our lifetimes. And it will be a final decision."
And he said the changes Britain wanted "do not fall in the box marked 'impossible'.
"They are eminently resolvable, with the requisite political will and political imagination."
How European leaders reacted
A spokesman for European Commission President Jean-Claude Juncker said Mr Cameron's benefit restriction proposals were "highly problematic" as they affected the "fundamental freedoms of our internal market" and amounted to "direct discrimination between EU citizens".
But he said the Commission viewed the letter as the starting point of negotiations and it would work with the PM for a "fair deal for Britain which is also fair for all the other member states".
German Chancellor Angela Merkel said "we want to work through these proposals with the aim of working towards a solution".
"Some points are more difficult than others, but given that we are working in the spirit of wanting to reach a solution, I am reasonably confident that we can succeed. Germany will certainly do its bit to help as far as European rules permit," she added.
In focus: The Cameron letter to Tusk
David Cameron's letter to Donald Tusk says the UK will not stand in the way of further eurozone integration but calls for safeguards to protect British business from discrimination and a formal recognition that the EU has more than one currency.
It says: "Our concerns really boil down to one word: flexibility."
On immigration, the letter calls for a "crackdown on the abuse of free movement", including longer re-entry bans for fraudsters and those who engage in "sham marriages" - and stronger powers to deport criminals.
People coming to the UK "must live here and contribute for four years before they qualify for in-work benefits or social housing", writes Mr Cameron.
The PM says he hopes the letter will "provide a clear basis" for reaching a "legally-binding and irreversible" agreement and "where necessary have force in treaties".
If an agreement can be reached on his four demands, Mr Cameron tells Mr Tusk: "I am ready to campaign with all my heart and soul to keep Britain inside a reformed European Union."
Foreign Secretary Philip Hammond told BBC's Newsnight that he believed treaty change would be needed. He also said the government was open to ideas about how to reduce migration to the UK.
He said: "Limiting access to welfare benefits is not an end in itself, it's a means to an end - we're trying to reduce the attraction of Britain to European migrants by reducing their access to benefits. What we're really trying to do is to reduce migration of European low-skilled people into the UK."
He added: "If the Commission comes back to us with alternative ways of doing that, of reducing the flow of those migrants into the UK, we'd certainly listen to any proposals they have to make."
What Eurosceptics said about the letter
The Vote Leave campaign said Mr Cameron's negotiating demands were "trivial" and that the only way for the UK to regain control of its borders and democracy was by leaving the EU.
Eurosceptic Conservative MPs criticised the prime minister's demands during a Commons debate, with backbencher Bernard Jenkin drawing gasps from MPs by asking: "Is that it?"
John Redwood said Mr Cameron should be asking for "much more" and there was nothing in Mr Cameron's speech to suggest Britain would get "anything like the protection we need" from European laws.
"It's about more than borders and migration," he added, "it's about who governs."
UKIP Leader Nigel Farage said it was clear Mr Cameron "is not aiming for any substantial renegotiation", with "no promise to regain the supremacy of Parliament, nothing on ending the free movement of people and no attempt to reduce Britain's massive contribution to the EU budget".
What those who want Britain to stay in EU said
Labour's shadow chancellor John McDonnell said Mr Cameron's position on the EU was "a lot of bluff and bluster" and more about "appeasing" some of his Eurosceptic backbenchers.
Labour's position was that Britain should stay in the EU and "negotiate our reform agenda as members of the club", he added.
The SNP said Mr Cameron had broken his promise to properly consult the Scottish government on the issue.
The party's European Affairs spokesman Stephen Gethins said: "During the Independence Referendum the prime minister claimed a Yes vote could mean Scots being thrown out of the EU - the reality is that it is his own policies that are taking us closer to the exit door than ever before.''
Will Straw, director of Britain Stronger in Europe, said: "Today the prime minister has set out a series of sensible and sound reforms to improve Britain's relationship with Europe. It is now clear that Leave campaigners are losing the argument."
Referendum on the UK's future in the European Union
The UK is to have a referendum by the end of 2017 on whether to remain a member of the European Union or to leave. The vote is being proceeded by a process of negotiations in which the Conservative government is seeking to secure a new deal for the UK.