During September, Mexican authorities opened some 2,403 murder investigations, a decline of 7 percent from the same month in 2018, and the lowest monthly total since April, according to the government figures. The months of July through September were the three most violent in 2018.
That could mark what government officials have called an inflection point, even though the number of murders remains on track to surpass last year's record total of 29,000.
The report comes as Mexican President Andres Manuel Lopez Obrador, a leftist who took office in December, has been on the defensive since drug gunmen rampaged through the northwestern city of Culiacan during a bungled attempt to arrest jailed drug kingpin Joaquin "El Chapo" Guzman's son.
The president has defended his policy of trying to dial down clashes with drug cartels to reduce murder rates.
The conservative opposition said the government's decision to release Ovidio Guzman during the Culiacan violence could encourage other gangs to push back against government forces.
Military police briefly arrested, then released Ovidio Guzman after being surrounded by cartel henchmen who launched attacks on security forces across town.
Lopez Obrador defended Guzman's release, and accused the opposition of trying to exploit the chaotic scenes in Culiacan to wage an "irrational campaign" against his government.
Had security forces attempted to hold Guzman against the cartel footsoldiers, many people could have been killed, Lopez Obrador told a regular news conference.
"Not just the criminals, who are also human beings, the soldiers, who we must protect," he said, "but (also) civilians." "I always have great belief in the wisdom of the people, and I know that the majority of Mexicans supported the government's decision," the veteran leftist said.
More than 200,000 people have been killed in the bloodletting since then-President Felipe Calderon sent in armed forces to crack down on drug gangs at the end of 2006.