MEXICO CITY—A weekend of coordinated violence convulsed Mexico’s second-largest city and a famed beach resort town in the latest sign of the emergence of a powerful and aggressive drug cartel.

Soldiers and police in Jalisco state searched on Sunday for three soldiers who have been missing since gunmen presumed to belong to the Jalisco New Generation Cartel shot down a Mexican army helicopter on Friday, killing three soldiers and injuring 12.

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