The new deaths came on the heels of a Saturday cartel attack on the northern Mexican city of Villa Union that left 10 gunmen and four police officers dead - and the local municipal building riddled with bullet holes.
Another six people were were injured, Solis added.
The government says the gang mounted an hour-long battle with security forces before fleeing along paths into rugged terrain.
Authorities apprehended 14 vehicles with powerful weaponry, according to the governor.
The shootout occurred just days after US President Donald Trump said he would designate Mexican cartels as foreign terrorist organizations, adding that the US had offered to "go in and clean it out", but the Mexican government had "rejected the offer".
Speaking outside the bullet-ridden town mayor's office, Governor Riquelme told reporters the state had acted "decisively" to repel the gunmen.
Riding into town in a convoy of heavily armed pickups, gunmen sprayed the offices of the mayor of Villa Union with bullets and fought police for more than an hour.
"I don't think that Mexico needs intervention".
During a speech in front of tens of thousands of supporters on his first anniversary as president, Lopez Obrador again said Mexico would handle its security problems, in a nod to Trump's comments earlier in the week. While pledging to act decisively against the gangs, he said that Mexico needed "collaboration and cooperation", not intervention from overseas.
But, "we won't allow organized crime to come to the area", he said.
Trump on Tuesday said he planned to designate the cartels as terrorist organizations, sparking concerns the move could serve as a prelude to the United States trying to intervene unilaterally in Mexico.
Lopez Obrador took office a year ago pledging to pacify the country after more than a decade of gang-fueled violence.
US Attorney General William Barr is scheduled to visit Mexico next week to discuss the issue.
Criticism has focused on the Nov 4 massacre of nine women and children of US-Mexican origin from Mormon communities in northern Mexico, and the armed forces' release of a captured son of drug lord Joaquin "El Chapo" Guzman under pressure from cartel gunmen in the city of Culiacan.
But Coahuila state itself had been relatively free of the worst of the violence in the most recent years.
Homicides reached record levels in Mexico last year and are on track to surpass that total this year.