Once a relatively small criminal operation that operated in the countryside and trafficked in stolen cars, the gang expand its criminal activities in the chaotic months following the president’s assassination, said Mr. Jean, the human rights group director. By forging alliances with other armed groups, it was able to control an area stretching from the east of Port-au-Prince to the border with the Dominican Republic — a territory so vast that the police are unable to pursue gang members.

“The police are in a situation of powerlessness,” Mr. Jean said.

The 400 Mawozo gang accounted for 60 percent of the kidnappings from July to September, Mr. Jean said. They are held responsible for kidnapping five priests and two nuns this year, and are also believed to have killed Anderson Belony, a well-known sculptor who had worked to improve his community, according to local news reports.

Gangs have gained so much power that they have taken on a nearly institutional role in some communities, stepping in for the police or providing basic services like road cleaning, said Mr. Vorbe, the political party leader.

“​​They have stepped in for the state,” he said.

The growing gang presence, and now the attack on a group of missionaries, have cast a pall over other aid organizations and projects in the country.

In Fond Parisien, about 20 minutes from where the kidnapping took place, is another mission project called Redeemed Vocational School, which teaches trades like auto mechanics, sewing, and computer skills. The group had been planning to build a larger school building, but the violence has made it harder to travel and get supplies, said Kenlyn Miller, 46, the chairman of the school’s board in Gambier, Ohio.

“Usually we have some Americans travel over to help with some of that,” he said, “and just because of the safety issues, that is probably not going to happen for quite a while. This definitely will put a damper on what can be done.”

“It puts fear in a lot of people, when they hear about this,” he said.

Adam Goldman and Elizabeth Dias contributed reporting.

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