Still, community leaders are so fearful their youths may follow the Islamic State’s propaganda that, during a 90-minute meeting with more than 60 local leaders, police officers and advocates, they pressed Mr. Johnson to prove the government is sincere in its offers of help.

Lila Al Sibai, a 28-year-old mother of three young children and a member of the cultural center’s board, asked for a $4 million federal grant to build a new gym and classrooms for the facility. “We need to have more activities for our youth,” she said after the meeting in this suburb of Columbus, which is the home of the country’s second-largest Somali-American community, behind only Minneapolis.

Mr. Saqr, the youth coordinator, suggested that Mr. Johnson’s agency offer a prize to the best countermessage to the Islamic State’s propaganda.

“Our youth are being hoodwinked and hijacked by their rhetoric,” he said. “We cannot just say ISIS is bad. That’s not an option. We need an outlet.”