David Cameron has promised to crack down on Islamic State (IS) sympathisers, stressing in a New Year's message that all Britons should have "loyalty" to their country.
The Prime Minister said 2016 would be a "test of our mettle" as he pledged action to tackle the "poisonous narrative" which led some Britons to turn against their country.
He said the UK should "revel" in its way of life rather than "appease" extremists, and all who live in the country must sign up to its values.
As well as pledging to tackle the "deep social problems" which have "blighted our country for too long", Mr Cameron also highlighted his drive for reform in Europe, ahead of a referendum which could take place this year.
The Prime Minister said: "These are the big challenges of our age, some of the biggest our nation has ever faced and this year is a test of our mettle - whether we put up with poverty or put an end to it; ignore the glass ceiling or smash it; abandon the tenant or help make them a homeowner; appease the extremist or take apart their ideology piece by piece.
"We will get Britain a better deal in Europe, give families the peace of mind they crave and we will make our country even more secure."
Mr Cameron, who has previously warned of the dangers posed by people in Britain who "quietly condone" IS's extremist ideology without explicitly supporting violence, reinforced his message that it was not only the gunmen and bombers who needed to be tackled.
He said: "When our national security is threatened by a seething hatred of the West, one that turns people against their country and can even turn them into murderous extremists, I want us to be very clear: you will not defeat us.
"And we will not just confront the violence and the terror; we will take on their underlying poisonous narrative of grievance and resentment.
"We will come down hard on those who create the conditions for that narrative to flourish.
"And we will have greater confidence in, indeed we will revel in, our way of life.
"Because if you walk our streets, learn in our schools, benefit from our society, you sign up to our values - freedom, tolerance, responsibility, loyalty."
The Prime Minister hopes to reach agreement with EU leaders on his demands for reform at a crunch summit in Brussels in February, and has hinted that the promised referendum could be held this year if he secures a deal.
He said: "I am negotiating hard to fix things that most annoy British people about our relationship with the EU.
"There is just one thing that drives me: what is best for the national interest of our country?
"But in the end it will be for you to decide: is our economic and national security in a dangerous world better protected by being in or out?"
Mr Cameron set out his desire to tackle a series of deep-rooted social problems in a year he has described as a potential "game changer" for the UK.
"With economic renewal and social reform we can make everyone's lives more secure," he said, promising action to boost home ownership and end discrimination.
In a separate written message, Mr Cameron said Britain begins the year with "renewed strength", striking a markedly more optimistic tone than in his missive last year when he warned the country faced ''chaos'' if there was a change in the economic course.
Mr Cameron appeared to take a swipe at his Labour opposite number, Jeremy Corbyn, insisting that while "others are on protest march, we remain on the long walk to a Greater Britain".
"There are many people who will tell you how deeply they care about these issues. They will shout into megaphones, wave banners and sign petitions," he said.
"But we're the ones who are able to make the arguments and take the difficult decisions in order to defeat these social scourges and deliver real security."
Mr Corbyn used his New Year message to claim 2016 would put Labour on course for government.
Vowing to continue his resistance to austerity, the Labour leader insisted 2016 "will be the start of a journey to deliver a Labour government in 2020 - a Labour government that will deliver a fairer, more just, more prosperous society that we can all enjoy".
Liberal Democrat leader Tim Farron used his message to argue "Britain deserves better" as he criticised the Tories and Labour for being divided parties.
Mr Farron insisted his party, which was all but wiped out in Westminster at the general election, would enter 2016 with a "a new sense of purpose, a new drive and a sense of ambition".