Meanwhile, an unspecified number of people were also missing, including some who were at the mayor's office, the governor said.
The Coahuila state government says lawmen are still chasing remnants of the presumed cartel force that attacked the town of Villa Union on Saturday.
Rapid gunfire could be heard on graphic video footage of the clash which was posted on social media. He said they were members of the Cartel of the Northeast, which is from the neighboring state of Tamaulipas.
Riquelme said authorities had identified 14 vehicles involved in the attacks and seized more than a dozen guns.
Lopez Obrador said Mexico would handle the problem, a view echoed by Riquelme as he spoke to reporters, Reuters reports.
"I don't think that Mexico needs intervention".
The events in Villa Union add to a series of recent security lapses that have raised doubts about the containment strategy of President Andres Manuel Lopez Obrador, who took office a year ago pledging to get a grip on chronic gang violence. "I think Mexico needs collaboration and cooperation", said Mr Riquelme, whose party is in opposition to Mr Lopez Obrador.
Lopez Obrador said on Friday he would not accept foreign intervention in Mexico to deal with the cartels in response to Trump's comments earlier in the week.
Tensions between the two countries intensified last week when President Trump announced he plans to designate the Mexican cartels as terrorist groups and "start hitting them with drones".
More than a dozen people were killed in a gunfight between armed civilians and the Mexican security sources near the USA border in northern Mexico, according to local media on December 1.
A tweet from Riquelme, translated roughly into English, said: "In the face of today's aggression, we immediately went to the municipality of #VillaUnión in solidarity with Mayor Narcedalia Padrón Arizpe, to give the population peace of mind and strengthen the actions of #seguridad in the north of Coahuila". Mexico's Secretary General of National Public Safety said there have been 29,414 homicides so far in 2019, Fox reported.
The November slaughter by Mexican drug cartel gunmen of three women who held USA citizenship and six of their children focused world attention on the rising violence.
Coahuila has a history of gang violence, although the homicide total in the state that borders Texas is well below where it was seven years ago.