David Cameron has urged other EU leaders to support his "reasonable" proposals for far-reaching curbs on welfare benefits for migrants.
Britain's prime minister said lower EU migration would be a priority in future negotiations over the UK's membership and he would "rule nothing out" if he did not get the changes he wanted.
Under his plans, migrants would have to wait four years for certain benefits.
Brussels said the ideas were "part of the debate" to be "calmly considered".
Mr Cameron said he was confident he could change the basis of EU migration into the UK and therefore campaign for the UK to stay in the EU in a future referendum planned for 2017.
But he warned that if the UK's demands fell on "deaf ears" he would "rule nothing out" - the strongest hint to date he could countenance the UK leaving the EU.
BBC political editor Nick Robinson said Mr Cameron's welfare curbs were "a tougher version of an approach already set out by Labour and the Liberal Democrats".
The main proposals in the speech - which are dependent on Mr Cameron remaining in power after May's general election - are:
- Stopping EU migrants from claiming in-work benefits, such as tax credits, and getting access to social housing for four years
- Stopping migrants claiming child benefit for dependents living outside the UK
- Removing migrants from the UK after six months if they have not found work
- Restricting the right of migrants to bring non-EU family members into the UK
- Stopping EU jobseekers claiming Universal Credit
- Speeding up deportation of convicted criminals
- Longer re-entry bans for beggars and fraudsters removed from the UK
- Stopping citizens from new EU entrants working in the UK until their economies have "converged more closely".
- Extra money for communities with high levels of migrants
Mr Cameron ruled out a temporary cap on migrant numbers or an "emergency brake" on EU freedom of movement rules, ideas both mooted in recent months, saying this would be less "effective" than reducing the incentives for people to come to the UK.
And he said there was "no doubt" his proposals would require changes to the treaties governing the European Union, necessitating the support of all EU members.
View from Poland
By Adam Easton, BBC Warsaw correspondent
David Cameron's speech has made headlines in Poland, with commercial news channel TVN24 leading on the story on its website.
But the speech has not provoked the outrage here that his comments on the BBC's Andrew Marr show in January did.
Then Mr Cameron specifically mentioned Poles when he spoke about the need to crack down on EU immigrants claiming benefit payments in the UK. Polish government officials said his words "stigmatised" Poles and were discriminatory.
This time around, Mr Cameron called the Polish Prime Minister Ewa Kopacz beforehand to apprise Warsaw about his speech.
The government here does not oppose moves in the UK to close benefit payment loopholes but Warsaw wants London to do it in a way that is non-discriminatory and in line with EU regulations.
I watched the speech with students at Torun's Copernicus University. Several told me they planned to go to the UK following their studies. None said the proposed benefit restrictions would put them off as they planned to work, not claim benefits.
Mr Cameron began his speech by saying migration had benefited the UK and that he was proud of the "multi-racial" nature of modern Britain.
But he said immigration levels in recent years - the largest in peacetime, he said - had put unsustainable pressure on public services and demands for change were "not outlandish or unreasonable".
"The British people will not understand - frankly I will not understand - if a sensible way through cannot be found, which will help settle this country's place in the EU once and for all."
Mr Cameron, who spoke to German Chancellor Angela Merkel and EU Commission President Jean-Claude Juncker before the speech, said he wanted the package to be adopted across the EU but that if it was not, he would seek a new UK-only arrangement.
By BBC political correspondent Chris Mason
Consider both the statistical and political imperatives that drove the prime minister to make this speech.
First, the numbers - 260,000 more people arrived in the UK in the year to June than left.
That is roughly the population of Sunderland turning up inside 12 months, needing houses, jobs, school places and doctors' surgeries.
Second, the politics. One word will do - UKIP.
David Cameron needed to combine the two Rs in his speech: being seen as simultaneously radical and realistic.
Bold enough to prove he gets what many see as a problem, believable enough to ensure he achieves what he sees as a solution.
And he did it by deploying a line a certain women's hair shampoo product would be proud of. Do a deal with us Europe, because we're worth it.
At the moment EU citizens are free to come to the UK and compete for jobs without being subject to any immigration controls. Those from outside the EU face much tighter controls if they wish to enter the country.
Outlining proposed restrictions on tax credits and child benefits, Mr Cameron said a migrant in work with two children was getting £700 a month on average in support from the state, twice the amount paid in Germany and three times as much as in France.
"No wonder so many people want to come to Britain," he said, adding that changes to in-work benefits could affect about 400,000 people.
Dr Carlos Vargas-Silva, a migration expert at Oxford University, told the BBC there were an estimated 50,000 EU migrants claiming tax credits who have been in the UK for fewer than four years, adding that the changes could have a real impact.
Mr Cameron also responded to criticism that the Conservatives' stated aim in its 2010 manifesto to reduce overall levels of net migration below 100,000 was "in tatters".
The PM acknowledged the goal would not met by May, blaming the economic weakness in the eurozone, and said "more time and work" was needed to accomplish it.
Home Secretary Theresa May said: "We are very clearly saying that we have not achieved that target."
Speaking on BBC Radio 4's PM programme, she also said there was "no set single right number" of immigrants that could come to the UK.
Tory MPs reacted positively to the speech but several urged him to go further.
Jacob Rees-Mogg said Mr Cameron's language indicated "he is willing to campaign to leave [the EU] and I believe that strengthens his negotiating position substantially".
But Bill Cash said the proposals did not go far enough, while another Conservative MP, Nigel Mills, said an outright cap on numbers was needed.
Labour leader Ed Miliband said Mr Cameron had made a "no ifs, to buts" promise at the last general election to get migration down and he had "no credibility" on the issue.
UKIP leader Nigel Farage said the prime minister should have apologised for missing his immigration target, and said he was "playing catch-up" with UKIP.
Liberal Democrat leader Nick Clegg said some of the proposals were "sensible and workable" but said there were "very serious question marks" over others, including deporting jobseekers after six months if they had not found work.
European Commission spokesman Margaritis Schinas said the proposals would have to be "examined without drama".
"It is up to national lawmakers to fight against abuses of the system and the EU law allows for this," he added.
In a statement, the German government emphasised the importance of free movement of people but said it was prepared to work with the UK to find "mutually acceptable solutions".