Two U.S. citizens were fatally shot by gunmen on Wednesday night in western Mexico, local officials said, a setback to the Mexican government’s efforts to curb the violence gripping several regions in the country.

The attack in Angamacutiro, a town in the state of Michoacán where drug gangs have battled to dominate the local economy and drug-trafficking routes, comes after several other high-profile killings and abductions in the area.

The couple — identified by Mexican prosecutors only as Rafael C., 53, and María Gloria A., 50, — were both residents of California and arrived in late November to spend the holidays with family, said Magdalena Guzmán, a press officer at the Michoacán prosecutor’s office. Mexican officials do not typically reveal the full names of crime victims in order not to obstruct investigations.

Prosecutors said the man had been born in the United States and the woman was a naturalized American born in Mexico. Ms. Guzmán said there was no immediate information about why the couple had been targeted.

The authorities learned of the attack after security officers found the couple’s bullet-ridden vehicle on a street in Angamacutiro. Inside was the body of the woman, who died at the scene, officials said. The man, found alive but gravely wounded, was taken to a nearby hospital, where he died early Thursday, Ms. Guzmán said.

A spokesman with the United States Embassy in Mexico said officials were “aware of the situation” and tracking it closely. The State Department said in a statement: “We are aware of reports of the death of two U.S. citizens in Michoacán, Mexico. We are working to gather more information and stand ready to provide consular assistance if needed.”