Mr Cameron said extremism grew out of a “warped worldview” that left Islamists believing that “9/11 was actually inspired by Mossad”.
Such views are at the root of jihadist and neo-Nazi ideology, he added.
Lord Ahmad, minister for countering extremism, said: “Now is the time. The issue has gone beyond the realms of something that can be looked at with tinkering. This needs a comprehensive, strategic approach.
“It needs leadership and direction, and who better to do it than the PM. He understands the challenge.
“I know the deep concern we have had in government about the rise of antisemitism. We have to be very clear that we are dealing with all of it in all its ugly guises.”
The Community Security Trust’s deputy communications director Dave Rich praised the “landmark” speech.
Mr Rich said CST had stressed to officials the importance of tackling antisemitism as part of counter-extremism policy since the terror attacks in France and Denmark earlier this year.
He said: “What happened in Paris and in Copenhagen really made the penny drop for the police and government. The jihadi terrorist threat to Jews and the jihadi terrorist threat to the wider community are not two separate issues.
“It was gratifying to see it as a central strand in the speech. It was a more highly-developed, detailed, nuanced explanation than we have ever seen.”
Mr Rich said Mr Cameron had understood the principles of CST’s concerns for many years. But government ministers had increasingly responded to the Jewish community’s worries with “a lot of understanding and empathy” since Jews were killed in the Paris attacks.
The Board of Deputies said British Jews would “welcome a robust approach to tackling the problem”, but called for a focus on online extremism.
Mr Cameron also appeared to suggest Islamist hate speakers on campuses should be treated in the same way as Holocaust deniers such as David Irving.
He added: “We’ve got to show that if you say ‘yes I condemn terror — but the kuffar are inferior’, or ‘violence in London isn’t justified, but suicide bombs in Israel are a different matter’ — then you too are part of the problem.”
But there was criticism of the speech from the Movement for Reform Judaism’s rabbi Laura Janner-Klausner. Speaking on the BBC’s Today programme, she said: “I appreciate Mr Cameron’s robust response to antisemitism and the protective references to Jews. But I also worry when this kind of language sits alongside a very different image of British Muslims.”
Before giving his speech in Birmingham, Mr Cameron visited the city’s King David Jewish primary school, where the majority of pupils are Muslim.
