Radical preachers will be banned from posting material online and anyone with convictions for extremist activity will be barred from working with children.
Deradicalisation classes will be made mandatory for others deemed a threat.
But Muslim leaders warned the strategy "continues down a flawed path" and risks "alienating" Muslims in the UK.
Also among the measures within the counter-extremism strategy are:
Prime Minister David Cameron said the plan would work because it was "comprehensive" .
"It's no good leaving this simply to the police or the intelligence services. It's no good simply talking about violent extremism. We need to confront all extremism," he said.
He said its effectiveness would be measured by whether people were being turned away from extremism, stopped from travelling to fight for IS, and by having "more cohesive and integrated communities".
Home Secretary Theresa May said non-violent extremism could not go "uncontested" as it led to the erosion of women's rights, the spread of intolerance and bigotry and the separation of some communities "from the mainstream".
She said that applied to neo-Nazi extremism just as much as Islamist doctrine.
The Muslim Council of Britain has released a highly-critical statement in response to the plans.
Secretary general Dr Shuja Shafi said the strategy would "reinforce perceptions that all aspects of Muslim life must undergo a 'compliance' test to prove our loyalty to this country".
"These measures could be seen more as a means to address the anxieties a minority of people may have against Muslims and their religious life, rather than the scourge of terrorism itself," he said.
Dr Shafi also said he detected "McCarthyist undertones" in the plans to create blacklists and exclude and ban people those deemed to be extremists.
Mr Mohammed Shafiq, chief executive of the Ramadhan Foundation, said the announcement was a "missed opportunity to really engage the Muslim community".
But Fiyaz Mughal, director of the interfaith Faith Matters organisation, said there was much in the plans that could "help in the battle against those who promote extremism".
Robin Brant, BBC political correspondent
At the heart of this considerable strategy on counter extremism are two significant challenges for the prime minister: the internet and the law.
Getting inciteful content off the web and getting "counter narrative" content up there is key to harnessing the full potential of a medium that IS has already mastered.
There has been much focus on the mosques but bedroom radicalisation is something the prime minister and MI5 worry intensely about.
The process of trying to persuade Facebook, Twitter and other social media giants to help is ongoing.
On the second point, the plans to introduce new powers to restrict what extremists can do and where they can go are still in their legal infancy.
The government concedes they will need to be properly targeted. It is still consulting with lawyers and community groups to try to get the balance right.
Police estimate at least 700 people from the UK have travelled to support or fight for jihadist organisations in Syria and Iraq, such as the so-called Islamic State, and the government believes tackling non-violent extremism is key to stemming the flow of people.
Parents of children aged under 16 have had the power to request the cancellation of passports - even where a child has taken or hidden the actual document - since July.
That power is being extended to parents of 16 and 17-year-olds, allowing families to contact a passport office where officials will investigate their concerns before a final decision is taken by the home secretary.
Mrs May said the measure had only been used by "a small number" of parents since July, but it was part of a package of new powers that would help tackle extremism.
Shadow policing minister Jack Dromey said it was "crucial we get the balance right" and that Mr Cameron must "be very careful not to use the language he used earlier in the summer that somehow the Muslim community is not standing up to terrorism".
Liberal Democrat leader Tim Farron said the announcements amounted to "rhetoric that may well divide communities and make our job of working with those communities to find and isolate terrorists and potential terrorists that much harder".
The home secretary has vowed to "systematically confront and challenge extremist ideology" as she detailed new curbs on those who "spread hate".