LONDON — Faced with growing alarm about Islamic militants who have made Britain one of Europe’s most active bases for terrorist plots, Prime Minister David Cameron has mounted an attack on the country’s decades-old policy of “multiculturalism,” saying it has encouraged “segregated communities” where Islamic extremism can thrive.

Speaking at a security conference in Munich on Saturday, Cameron condemned what he called the “hands-off tolerance” in Britain and other European nations that had encouraged Muslims and other immigrant groups “to live separate lives, apart from each other and the mainstream.”

He said the policy had allowed militants leeway to radicalize young Muslims, some of whom went on to become terrorists, and that Europe could not defeat terrorism “simply by the actions we take outside our borders.”

“Europe needs to wake up to what is happening in our own countries,” he said. “We have to get to the root of the problem.”

In what aides described as one of the most important speeches since he became prime minister, Cameron said the multiculturalism policy — one espoused by British governments since the 1960s, based on the principle of the right of all groups in Britain to live by their traditional values — had failed to promote a sense of common identity centered on values of human rights, democracy, social integration and equality before the law.

Similar warnings about multiculturalism have been sounded by Chancellor Angela Merkel of Germany and by President Nicolas Sarkozy of France. But, if anything, Cameron went further. He called on European governments to practice “a lot less of the passive tolerance of recent years and much more active, muscular liberalism,” and said Britain would no longer give official patronage to Muslim groups that had been “showered with public money despite doing little to combat terrorism.”

Muslim groups in Britain were quick to condemn the speech.