Omar Sheikh was a promising LSE student from a comfortably middle-class Anglo-Pakistani family. On a humanitarian mission to Bosnia in 1992, he was recruited into a life of terror. In July 2002, he was sentenced to death in Pakistan for his role in the beheading of an American journalist, Daniel Pearl.

In his book “Who Killed Daniel Pearl?” Bernard-Henri Levy recounts young Omar’s reaction to the suggestion that he go to Afghanistan for training. He imagines him thinking “… he has to finish his studies … and his father is still the one who decides everything.”

“We’ll talk to your father,” he is told by the Islamist he meets in Bosnia. “I’ll organise a meeting for him with Maulana Ismail, imam of the Clifton mosque, a holy man, who is experienced at guiding young English Muslims to our places in Afghanistan and who will find the words to convince him, I’m sure. It’s an honor for a family to have a son who abandons his useless studies to consecrate himself to the life of jihad.”

Thus was a bright student from a good family lured into a holy war that aims to impose Islamist fundamentalism on the world.

It is a war fought with planes crashed into buildings or blown up in midair, roadside bombs, kidnappings, beheadings, and other unspeakable instruments of terror. It is decentralized but global in scope, from madrassas in Pakistan, to mosques in London, to “charities” in America, to banks and boardrooms in the Middle East. It is a war with a cultural and ideological component that is lavishly financed by easy oil money from states like Saudi Arabia that we have long (and foolishly) regarded as “moderates” and “friends”. It is a war utilising sophisticated technology for destruction and communications, and equally sophisticated techniques for inculcating lethal extremism.

The warriors in this jihad are identified, indoctrinated and recruited by men who manipulate the power of faith to induce a fanaticism whose ultimate expression is the martyrdom of suicide missions. Among them are clerics who have rewarded their welcome into our liberal, open societies by preaching our destruction. How many acts of holy war – how many recruitments? – were performed by the imam who carried out his assigned task of facilitating Omar Sheikh’s training at an al-Qaeda camp in Afghanistan? By what concept of liberal democracy must we allow these clerics who are out to destroy us the opportunity to reach impressionable young people with their message of holy war?

It has always been difficult to draw the fine line between protected speech, which is fundamental to our individual liberty, and incitement to prohibited criminal activity. In the United States, that line has long been defined by the concept of a “clear and present” danger. You don’t claim the right to shout “Fire!” in a crowded theatre as a matter of free speech. In the U.K., too, advocacy that falls short of incitement to immediate violence has been widely tolerated. But combating Islamist extremism may require rethinking the idea of imminence in judging the dangers, and the appropriate response to them, of the insidious process leading ultimately to acts of mass murder. It is the act of recruitment into the swamp of a world divided into believers and infidels that may well be the more appropriate line dividing acceptable from unacceptable advocacy.

Yet in both the U.K. and the U.S. we have been reluctant – dangerously so – to restrict, and in many cases even to monitor, what is said in the mosques and social centres of Islamist extremists.

In both our countries, there is great resistance to the effective surveillance of extremist Islamist groups. Opposed by most Muslim and civil liberty organisations, which fear that official scrutiny will lead to harassment and discrimination, police authorities have found it difficult to gather essential intelligence that could give timely warning of the formation of cells and networks destined to plan and execute acts of terror.There was a (largely partisan) outcry in the U.S. when it was learned that telephone conversations and bank transfer records were being scrutinised for terrorist connections, even though not a single aggrieved individual could be found. The occasional, inevitable mistakes by over-worked police and security organisations have further inhibited aggressive surveillance.

After 9/11, 7/7, Madrid, Bali and the rest, all carried out in the name of jihad, and after the chilling discovery of the successfully foiled plot to destroy thousands of air travellers last week, it is obvious we need to know what is going on in those parts of the Muslim community where Islamist extremists have made inroads. At the same time, we need to encourage the vast majority of Muslims who do not share jihadist views to join in opposing them.

To gain the trust and confidence of the American and British Muslim communities, officials in both countries have “outreach” programmes to work with mainstream community leaders. Sadly, these programmes have often left the silent majority of moderate, tolerant Muslims on the sidelines while courting organisations and leaders who are doing more for the disease than the cure. In an important study released by the British think tank Policy Exchange, “When Progressives Treat with Reactionaries,” Martin Bright has described what he calls “the Government’s bizarre dalliance with the Islamists”. Based on leaked official documents, Bright demonstrates convincingly the Foreign Office’s eagerness to work with, and inevitably enhance the standing of, representatives of the Muslim Brotherhood, an organisation committed to holy war (“Jihad is our way. Dying in the way of Allah is our highest hope”), as well as individuals who have openly supported suicide bombing. Inexplicably, the British Government has accepted as its main partner on Muslim issues the Muslim Council of Britain despite “the clear Islamist sympathies of its leaders”.

Something similar has happened in the U.S., where extremist leaders claiming to speak for America’s tolerant Muslim community have been received at official events. On both sides of the Atlantic we need to abandon the illusion that extremist leaders are authentic and less voluble moderates are not. Talk to the latter — and keep a close watch on the former.

Mr. Perle is a fellow at the American Enterprise Institute. He served as assistant secretary of defense in the administration of Ronald Reagan.