The Home Office paper reportedly says schools, universities, local councils and charities are vulnerable to infiltration by extremists.
The Sunday Telegraph said the strategy document, which has not yet been published, calls for a review into how Islamic Sharia courts operate in Britain, a ban on radicals working with young children and changes to citizenship rules to promote “British values”.
The document reportedly says: “In the past, there has been a risk that the government sends an ambivalent and dangerous message – that it doesn’t really matter if you don’t believe in democracy.
“We need to stand up and be more assertive in promoting our values and challenging the extremists who fundamentally oppose them.
“This will include explaining our foreign policy (and) promoting mainstream voices supporting the quiet majority in all communities who oppose extremism.”
New policies suggested in the document include making job centre employees identify claimants who could be vulnerable to radicalisation, and a penalties scheme to make people on benefits learn English.
The paper suggests that the so-called Trojan Horse plot – where Islamists were accused of trying to infiltrate schools in Birmingham – was “not an isolated example of schools where extreme views became prevalent”.
It says universities, local councils and charities could being vulnerable to “entryism”, where people with extremist views purposely get into influential positions from where they can promote their values.
In November the government unveiled the Counter-terrorism and Security Bill, whose powers include a legal requirement by schools, prisons and councils to put in place policies or programmes to stop would-be extremists from being drawn into terrorism.
Other measures included the clarification of legislation to ensure insurance companies can no longer foot the bill for terrorist ransoms, blocking foreign fighters from returning to the UK and re-introduced powers to relocate terror suspects across the country.
Shadow home office minister Diana Johnson said: “As senior police officers warn about the scale of Theresa May’s cuts and whether they can deal with increasing challenges such as terrorism, more reheated words from the Home Office feels too little, too late.
“The Prevent programme, which is supposed to be tackling radicalisation and all forms of extremism in communities, has been downgraded by this government. The police are asking for more help and communities increasingly feel let down.
“Theresa May abolished control orders, weakened counter-terror powers, downgraded Prevent work and has failed to properly support the police, or communities, parents and local organisations who are trying to counteract radicalisation.
“We will look at the details of any policy that could help stop young people being drawn towards extremism, but with this Government the rhetoric rarely matches the reality.”