In a keynote speech in Birmingham, Mr Cameron unveiled details of a five-year strategy aimed at tackling the problem of Islamic extremists recruiting Muslims in the UK.
The Prime Minister also made it clear that while he wants to expand bombing raids against Islamic State (IS) from Iraq to Syria, he does not want troops on the ground there.
At the centre of the government’s strategy will be a scheme allowing parents, worried about their children joining IS, to apply for their child’s passport to be cancelled.
This followed the recruitment of Glasgow-born jihadist Aqsa Mahmood who was then accused of persuading three teenage girls from Bethnal Green in London to join the terrorist organisation.
Other measures will see Ofcom given the power to clamp down on cable TV channels broadcasting extremist messages, along with attempts to address the problem of radicalisation in prisons and online.
The government also announced range of other measures such as an engagement forum, the launch of a study looking at how extremism spreads and a consultation on the victims of forced marriages.
Mr Cameron said that too often the authorities had “turned a blind eye” to issues like forced marriage or female genital mutilation (FGM) for fear of offending cultural sensitivities.
Announcing the consultation on introducing lifetime anonymity for the victims of forced marriages, he said he wanted to see more prosecutions in cases of this sort as part of a drive to “enforce” British values and ensure they applied uniformly to people of all backgrounds.
“My argument with young people being sucked towards this appalling extremist Isil worldview is ‘You are heading towards a belief system that believes in throwing people off buildings, raping children, enslaving women’,” said the Prime Minister.
“The values of freedom and democracy are far stronger, far better than the values of Isil.”
He also attacked the National Union of Students for “allying itself” with the Muslim advocacy group Cage, one of whose officials earlier this year described the IS terrorist nicknamed Jihadi John as a “beautiful young man”.
In a direct message to the students’ body, he said: “I want to say something to the National Union of Students. When you choose to ally yourself with an organisation like Cage, which called Jihadi John a ‘beautiful young man’ and told people to support the jihad in Iraq and Afghanistan, it really does in my opinion shame your organisation and your noble tradition of campaigning for justice.”
Mr Cameron said that the government will publish a new counter-extremism strategy in the autumn, setting out a range of actions in what he described as the “struggle of our generation”.
This will include action to “expose” extremism and to rebut conspiracy theories which accuse the West or Jews of seeking to destroy Islam or claim that Muslims are trying to take over the UK.
He said internet companies will be expected to go “much further” in protecting users from being exposed to extremist material.
And he announced a new review by Louise Casey into boosting opportunity and integration for minority groups.
A spokesman for the Islamic Human Rights Commission, Arzu Merali, said: “Cameron’s claims simply reinforce the now widely held prejudice that Muslim politics and practice are violently inimical to the society we live in.
“In fact, policy after policy from this and previous governments have forced Muslims into silence over valid claims whilst lauding a fictional idea of European supremacy over them and other beleaguered minorities. It is time for a push-back against this divisive and sinister narrative.”
And a spokesman for the Hizb-ut-Tahrir organisation, which campaigns for an Islamic caliphate, said: “Like his predecessors, Cameron conflates legitimate religious and political views that Muslims hold with the chaos that has been created in Iraq and Syria.”
But the Muslim Council of Britain said it supported “sound, evidence-based” measures that confront terrorism effectively.
SNP MP Tasmina Ahmed-Sheikh said: “It is vital that the UK government works hand in hand with the mainstream Muslim community to tackle terrorism at its root cause, especially by supporting Muslim families.
“There needs to be an inclusive approach.”