Cameron highlighted two cases this week – a 17-year-old from northern England who blew himself up in Iraq and three sisters who abandoned their husbands and are believed to be in Syria with their nine children – as examples of how people can slide from prejudice to extremism.

He told a security conference in Bratislava that people who for example believe democracy is wrong, women are inferior and religious doctrine trumps the rule of law share the ideology of Islamist extremists.

“There are people who hold some of these views who don’t go as far as advocating violence, but do buy into some of these prejudices giving the extreme Islamist narrative weight and telling fellow Muslims ‘you are part of this,'” he said.

“This paves the way for young people to turn simmering prejudice into murderous intent … Part of the reason it’s so potent is that it has been given this credence,” he added.

Cameron warned that a troubled boy or girl will find it less of a leap to go from British teenager to Islamic State fighter or wife if such beliefs are “quietly condoned online or perhaps even in parts of your local community”.

While the government has a role to play in tackling radicalisation, so too do communities and families, he said.

“We need to have a frank debate about the role that everyone has to play,” a source in Cameron’s office said.

“Part of this is encouraging people in those communities who want to help tackle this radicalisation of young people to come forward and help work together on this.”

In a commentary on Cameron’s speech, the Muslim Council of Britain said it was wrong to suggest Muslim communities had led young people to extremism.

“It has been suggested that Muslims are not doing enough and somehow condone extremism,” said Shuja Shafi, secretary general of the umbrella organisation representing some 500 groups in Britain. “We would argue that clear evidence should be presented and wrongdoing challenged, rather than perpetuate insinuation persistently.”

He called for Muslim communities, the government and wider British society to work together to tackle the problem.