"As a result of this confrontation, six people lost their lives," said Sonia de la Garza, the Durango state prosecutor, yesterday.
Mexican mayors have become frequent targets of crime groups with at least six killed so far this year, and 15 in 2010.
On Friday, a former mayor who had survived two assassination attempts during her 2008-2010 term was found dead in the western state of Michoacan, police said.
A hotel in the town of Gomez Palacios in Durango where police taking part in a counter-drug offencive were staying came under fire on Sunday by gunmen.
A stray bullet killed a child who happened to be passing in a car with his family, De la Garza said.
Durango has recently experienced a surge of drug-related violence as the Zetas crime group moves in on turf that had long been dominated by the Sinaloa drug cartel.
More than 60,000 people, many of them having nothing to do with organised crime, have lost their lives in a bloody war on drugs unleashed in December 2006 by President Felipe Calderon, whose term ends next month.