The clashes occurred on Monday after the “self-defense” vigilantes ignored a government order to quit their armed struggle against the Knights Templar drug cartel, according to the country's newspaper Reforma.
Seven civilians were killed in the town of Mugica as well as three soldiers and two civilians in Paracuaro, the daily reports.
The vigilante groups had taken up positions in communities around the city of Apatzingan, which is considered the stronghold of the drug cartel.
Mexican Attorney General Jesus Murillo Karam said on Tuesday it was too early to confirm a death toll, but said government troops would enter the region to “establish legal order.” Other reports say soldiers have shot dead at least three people, including an 11-year-old girl in the town of Antunez.
On Monday, Interior Minister Miguel Angel Osorio Chong urged vigilantes to lay down their weapons since emergency talks were underway in the Michoacan state capital, Morelia.
The growing civilian defense movement began last year in Michoacan in a bid to clear the area of the Knight Templar cartel members.
The towns formed the vigilante groups argued that local police were unable to stop the cartel’s kidnappings and murders.