JAKARTA, Indonesia—Support for Islamic State is quickly growing among Muslim extremists in Southeast Asia, and authorities worry they don’t have enough legal tools to keep them from spreading fundamentalist beliefs at home—or staging terror attacks.

Experts say the risk is highest in Indonesia. This nation of 255 million has the world’s largest Muslim population and a history of terror bombings carried out by an earlier generation of militants who trained with al Qaeda in Afghanistan in the 1980s. Authorities and analysts say hundreds of Indonesians, including entire families, have gone to Syria and Iraq to live in Islamic State territory and support its cause.

This is a striking change from what happened in Afghanistan, when mostly single males went to fight. Some of today’s volunteers aren’t necessarily fighters but professionals with specialized skills who have traveled to the Middle East with their wives and children to build new lives. “They have no intention of ever coming back,” said Sidney Jones, director of the Jakarta-based Institute for Policy Analysis of Conflict. “They are going to live and work in an Islamic State.”

Authorities worry that even those with no intention of leaving the radical Sunni group’s self-declared caliphate pose a threat by further inspiring hard-liners back home.

Indonesian President Joko Widodo said in an interview with The Wall Street Journal that Islamic State is Indonesia’s biggest international concern, and that it comes up in every discussion he has with other leaders. “When we have a meeting with a president or prime minister from another country, always they say that now the number one issue is ISIS,” he said. “Indonesia (is) also the same.”