The suspects apparently used a high-powered 50-caliber Barrett rifle to bring down the helicopter chasing them in Michoacan state on Tuesday, said National Security Commissioner Renato Sales.
"It was indeed shot down," Sales told Radio Formula, adding that authorities were "working to capture those responsible."
The pilot and three state police officers died at the site. The state prosecutor's office said a fourth agent succumbed to his injuries yesterday.
It is the second time since 2015 that a gang has downed a helicopter. Last year, the powerful Jalisco New Generation drug cartel in neighboring Jalisco state used a rocket launcher to hit a military helicopter, killing seven soldiers and a policewoman.
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A federal government source, who spoke on condition of anonymity because he is not authorized to speak publicly, told AFP that there is "suspicion that this cartel" also downed the aircraft in Michoacan.
The deadly incident near the village of El Chauz happened amid a resurgence of violence in Michoacan, a state once dominated by New Generation's rivals, the pseudo-religious Knights Templar drug cartel.
The confrontation took place in Michoacan's Tierra Caliente (Hot Land), a region that has endured years of drug violence and vigilante justice.
The helicopter crashed in a mountainous area where local farmers grow lime and mango.
Authorities manned checkpoints leading to the area of the incident, which was cordoned off with some 200 soldiers and police keeping guard.
The federal source said soldiers, marines and state police were hunting for suspects.
The Knights Templar terrorized Tierra Caliente until lime growers formed vigilante forces in 2013 to fight back against the gang, which murdered, kidnapped and charged the population protection taxes.
The cartel was weakened as authorities deployed troops and arrested or killed its top leaders, but smaller criminal groups have since emerged.
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