New laws to target radicalisation
David Cameron is to set out a string of new powers to tackle radicalisation, saying the UK has been a "passively tolerant society" for too long.
The PM will tell the National Security Council a counter-extremism bill will be in the Queen's Speech on 27 May.
The bill will include new immigration rules, powers to close down premises used by extremists and "extremism disruption orders".
Mr Cameron will say a "poisonous" extremist ideology must be confronted.
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The proposals were first set out by Home Secretary Theresa May before the general election.
But the Conservatives were unable to secure the backing of their then Liberal Democrat coalition partners for the measures.
There is likely to be some opposition in the new Parliament on the grounds that some of the plans could infringe people's right to free speech, BBC home affairs correspondent Danny Shaw said.
The measures are also expected to introduce banning orders for extremist organisations who use hate speech in public places, but whose activities fall short of it being proscribed as a terror group.
The banning orders and extremism disruption orders will work in a similar way to ASBOs, with police having to go to the courts to obtain them, a Downing Street spokesman said.
Analysis: BBC home editor Mark Easton
Under the proposals, ministers would be able to silence any group or individual they believe is undermining democracy or the British values of tolerance and mutual respect.
One can understand a government's determination to prevent extremism that might lead to radicalisation and terrorism. But where to draw the line? And indeed, how do we draw up a definition?
There is, it seems to me, an inherent contradiction between banning orders and the core British value that one should be tolerant of different viewpoints.
History tells us that the development of new ideas of governance and government require people to think radically. Extreme views are necessary to test the wisdom of the mainstream.
Would those who oppose homosexuality or multiculturalism or feminism be accused of threatening values of tolerance and equality? Could Russell Brand's argument against voting be regarded as threatening democracy?
Read more from Mark Easton here.
The home secretary is also looking at the possibility of tightening asylum rules for those who express extremist views, he added.
Extremism is defined in the government's prevent strategy as "vocal or active opposition to fundamental British values including democracy, the rule of law, individual liberty, mutual respect and tolerance of different faiths and beliefs. In addition, calling for the deaths of members of the armed forces".
Theresa May told BBC Radio 4 Today the government wants to "bring people together to ensure we are living together as one society".
She said: "What we are proposing is a bill which will have certain measures within it, measures such as introducing banning orders for groups and disruption orders for individuals, for those who are out there actively trying to promote this hatred and intolerance which can lead to division in our society and undermines our British values.
"But it will be part of a bigger picture , a strategy which will also have as a key part of it actually promoting our British values, our values of democracy, rule of law, tolerance and acceptance of different faiths."
The measures, she added, will focus on "extremism of all sorts... that is seeking to promote hatred, that is seeking to divide our society, that is seeking to undermine the very values that make us a great country to live in".
According to details given by Mrs May at last year's Conservative Party conference, such orders would apply if ministers "reasonably believe" a group intended to incite religious or racial hatred, to threaten democracy, or if there was a pressing need to protect the public from harm, either from a risk of violence, public disorder, harassment or other criminal acts.
The granting of a ban, which would be subject to immediate review by the High Court, would make membership or funding of the organisation concerned a criminal offence.
The extreme disruption orders could be imposed on individuals, using the same criteria.
BBC home affairs correspondent Dominic Casciani
Policymakers have debated the definition of extremism ever since Tony Blair's government looked at new laws after the 7/7 Tube and bus attacks in London a decade ago.
There are, potentially, two key challenges for the government in creating anti-extremism laws and tools.
First, can a definition of extremism that leads to someone facing restrictions, such as a ban on using social media, withstand legal challenges - particularly on human rights grounds?
Secondly can such bans work in practical terms without tying up the resources of the security services.
MI5, for instance, already has triage-like systems to prioritise watching the most dangerous people: it can't monitor everyone with dangerous views.
That aside, this package of measures is part of a potentially significant shift in focus.
Ministers want tools to marginalise, restrict and silence these voices because disrupting their influence may buy time to intervene and bring someone back from the edge before it's too late.
Read more from Dominic
Under the government's plans, the Charity Commission will be given more power to "root out charities who misappropriate funds towards extremism and terrorism", and broadcast regulator Ofcom will be able to take action against channels broadcasting extremist content.
The terror threat level was raised from substantial to severe last August in response to the conflict in Syria and Iraq.
Ministers responded by introducing new orders that can block British fighters from returning to the UK and give police the power to seize the passports of people suspected of plotting to join the fighting abroad.
Mrs May will tell the National Security Council - which meets weekly and is chaired by the prime minister - that the government will empower institutions to "challenge bigotry and ignorance".
Mr Cameron will say the new powers will make it harder for people to promote extremist views.
"For too long, we have been a passively tolerant society, saying to our citizens 'as long as you obey the law, we will leave you alone'," he will say.
"It's often meant we have stood neutral between different values. And that's helped foster a narrative of extremism and grievance."
The Conservative government will "conclusively turn the page on this failed approach," he will add, saying the UK must confront "head-on the poisonous Islamist extremist ideology".
Jonathan Russell from the Quilliam Foundation think tank, which challenges extremism, said the measures would tackle symptoms, not causes.
He told Today there was a danger of "negatively" altering the balance between national security and civil liberties.
And on the government's plans, he added: "I don't think it will tackle radicalisation. I don't think it will change the numbers of people who are attracted to this poisonous ideology. And I don't think it will attack the ideology itself."
Liberal Democrat foreign affairs spokesman Tim Farron said much of what is being proposed is too "woolly":
He added: "Somebody making a speech, which is critical of somebody else's point of view, is that a hate speech? There is no clarity on this."