Mr. Belmokhtar’s lucrative kidnapping business helped turn northern Mali into a destination for aspiring jihadis. Starting in 2004, radicalized youths flocked there from my native country of Mauritania, as well as from Algeria, Niger, Morocco, Nigeria and Saudi Arabia.

The cash infusion from ransoms allowed Mr. Belmokhtar and his acolytes to set up terrorist training camps and enabled them to buy locals’ support. By marrying into local families, and providing services to the desperately poor inhabitants of the Sahel region, they established themselves as a plausible alternative to Mali’s weak government.

By 2011, terrorists had effectively set up their own ministate in northern Mali. While aware of the ransom problem, the European Union was unable to formulate a united strategy to deal with it. As a result of dysfunctional multilateral institutions, each country continued to fend for itself and its own citizens.

THIS shortsighted approach destabilized the Sahel and angered the region’s most powerful nation, Algeria. For years, Algerian officials had complained about the impact of ransom payments on their own security. They went so far as to propose, in the United Nations General Assembly, a ban on paying ransoms to terrorists. The resolution became the basis of a Security Council resolution in 2009. But in practice, Algeria’s pleas went largely unheeded.

France’s recent military operation in Mali would not have been necessary if there had been a coherent European policy that involved targeted operations against terrorist networks. Even today, with French and African troops on the ground in Mali, there has been shockingly little help from other European governments. Most of Europe has avoided responsibility for preventing the emergence of a new terrorist hot spot virtually on its doorstep.

By contrast, the American government seems to grasp the seriousness of the problem and has gone to great lengths to stop it. The Treasury Department’s under secretary for terrorism and financial intelligence went to Europe last October, seeking to prevent any future ransom payments to A.Q.I.M. and a related group, Al Qaeda in the Arabian Peninsula. But the ransom problem is not, ultimately, America’s responsibility; Europe’s leaders must slay the monster they helped create.

That won’t be easy. The belief that Africa’s ill-prepared armies and France can make the problem of Islamist radicalism in North Africa disappear is a manifestation of European leaders’ delusional attitudes toward the region.

Europe owes the people of the Sahel — and European citizens — a commitment to refuse ransom money to terrorists anywhere. The only thing that Mr. Belmokhtar and his ilk should expect from the international community is overwhelming force of the sort Algeria demonstrated during the hostage crisis last month. Only by showing them that hostage-taking by terrorists is futile can security in the Sahel be re-established. Otherwise, another Mali is waiting to happen — somewhere nearby.