The total number of dead in the conflict is reported to be 54 people, according to local officials. This is a decrease from the figure of 80 dead reported last week.
The Colombian government has declared "war" on the armed guerrilla groups that have been fighting each other in the Catatumbo region, near the border with Venezuela. Around 10,000 soldiers have been deployed in the region.
The wave of violence is due to forces from the left-wing rebel group ELN and former members of the Farc guerrilla, with which the Colombian government signed a peace agreement in 2016, fighting, among other things, for control of the cocaine trade.
According to local authorities, all 13 people killed in the battles over the weekend are believed to be former Farc members.