Mr Cameron suggested there would be greater scrutiny of some Muslim groups which get public money but do little to tackle extremism.
Ministers should refuse to share platforms or engage with such groups, which should be denied access to public funds and barred from spreading their message in universities and prisons, he argued.
"Frankly, we need a lot less of the passive tolerance of recent years and much more active, muscular liberalism," the prime minister said.
"Let's properly judge these organisations: Do they believe in universal human rights - including for women and people of other faiths? Do they believe in equality of all before the law? Do they believe in democracy and the right of people to elect their own government? Do they encourage integration or separatism?
"These are the sorts of questions we need to ask. Fail these tests and the presumption should be not to engage with organisations," he added.
Going after Muslims here on their civil rights record is one thing, there are those who don't take kindly to European liberalism and do strive to abrogate the rights of women and non-Muslims. But if you look at Cameron's words, the first thought that crosses my mind is "Well, he must not be a fan of the Republican Party here, then."
I'm sure that's news to the Republicans. They fail all four of Cameron's questions, having voted against women's rights and calling America a Christian nation, doing everything they can to disenfranchise gays and other minorities legally, wanting to get rid of the 17th Amendment allowing people to elect Senators, and well, they're not real big fans of integration, either.
Does this mean that American Republicans are an extremist group in Britain? Someone should ask him.