WASHINGTON — American intelligence and law enforcement agencies have identified nearly a dozen Americans who have traveled to Syria to fight for the Islamic State in Iraq and Syria, the militant group that the Obama administration says poses the greatest threat to the United States since Al Qaeda before the Sept. 11, 2001, attacks.

As ISIS has seized large expanses of territory in recent months, it has drawn more foreign men to Syria, requiring more American and European law enforcement resources in the attempt to stop the flow of fighters, senior American officials said. And as a result of the increasing numbers of men, ISIS is now recruiting foreign women as jihadist wives.

ISIS has become more attractive to would-be militants because, unlike Al Qaeda, it has seized territory that it rules by strict Islamic law. “ISIS is able to hold itself up as the true jihad,” said a senior American official. “They’re saying: ‘Look at what we are doing, what we’re accomplishing. We’re the new face. We’re not just talking about it. We’re doing it.’ ”

ISIS’ attraction to some is based on its reputation for brutality. On Thursday, that reputation grew worse when it was revealed that it had waterboarded four hostages early in their captivity — including the American journalist James Foley, who was beheaded this month.