“This is classic trajectory into jihadist terrorism in Europe,” said Thomas Hegghammer, an expert on jihadist movements at the Norwegian Defense Research Establishment. “There is not a single pathway, but this one is very worrying. They are misfits who find a solution to their problems in radical Islam.”

In embracing violence in the name of Islam, Mr. Hussein, a former member of a Copenhagen criminal gang called the Brothas, “substituted one subculture for another,” Mr. Hegghammer said, adding, “The easier it is for someone to plug into this radical Islamic subculture, the more radicalized misfits you are going to have. At the moment, it is very easy.”

Announcing new measures on Thursday to fight terrorism, including extra funding for intelligence services, Danish officials did not mention religion while vowing to defend what Mette Frederiksen, the justice minister, described as “one of the most generous societies there are.”