MEXICO CITY — The island nation of Trinidad and Tobago has imposed a nightly curfew and sent troops to cope with a rash of violent crime associated with gangs, one of the starkest signs of worry in the Caribbean region over a spike in drug trafficking.

Prime Minister Kamla Persad-Bissessar, in a nationally televised address on Sunday night, announced what she called a “limited” state of emergency. It includes a 9 p.m.-to-5 a.m. curfew in major cities and towns and broader powers for the police to make searches and issue arrests, with 5,000 members of the military assisting them. Her speech followed a weekend of mayhem that left 11 people dead.

The measures have slowed the pace of drug-related killings and led to the arrest of 58 gang leaders, the foreign minister, Surujrattan Rambachan, said in a telephone interview on Wednesday.

“It’s a limited intervention to deal with gangs and get guns off the streets,” he said. He added that after about two weeks, the state of emergency could be extended for 90 days with approval from Parliament.