Ms. May said that the authorities needed to begin at home. “The first thing we must do is discourage young British Muslims from traveling to Syria and Iraq in the first place,” she said, but that is hardly easy, and such efforts do not seem to be working well, especially after the group, also known as ISIS, declared itself a caliphate.

Even now, the British police are trying to track down a 15-year-old girl from Bristol who they believe traveled to Istanbul with a 17-year-old girl from London with the intention of entering Syria to join the Islamic State. An assistant chief constable, Louisa Rolfe, said there were indications that the Bristol girl might have been “radicalized.”

There would be no penalties for the girls, but for adults, Ms. May said, it is illegal to fight for terrorist groups.

Belgium has been a prime recruiting area for jihadists. In Antwerp on Tuesday, the trial continued of 46 members of Sharia4Belgium, a radical Muslim organization accused of recruiting volunteers to fight in Syria. Of the group, nine are believed to be dead and 29 are in Syria, according to the Belgian newspaper Le Soir, which called the case “the most important terrorist trial that Belgium has ever witnessed.”

At least 300 Belgians have left for Syria, Ms. May said, along with 400 Germans. About 800 Russians are believed to be fighting in the region, along with 60 Australians, and at least 80 Swedes, 50 Norwegians and 70 Danes, according to estimates from various centers that study the topic. There are also fighters from Italy, the Netherlands and Spain.

Already, according to Mr. Neumann, about 40 percent of the 30,000 Islamic State fighters are foreign, though many of them are non-European. About 20 percent of the Nusra Front’s 10,000 fighters are foreign.

In France, Mr. Cazeneuve told Le Journal du Dimanche that 36 French citizens had died in the region, and that some returning jihadists boast about what they have done and “say they are ready to leave again.” He said that at least 70 people had been prevented from leaving after the authorities received about 350 alerts about possible jihadists, including 80 minors and 150 women.