The government has said 6,402 civilians died as part of this policy from 2004 to 2008, with slain civilians dressed up in guerrilla fatigues in some cases.
On Tuesday, the army asked forgiveness from the families of 19 of those who were part of the larger group.
"We acknowledge that painful acts were committed by members of the national army that should never have happened," army commander Luis Ospina said during an event in Bogota.
He said soldiers had "tainted the legitimacy" of the army. He added, as relatives of victims watched him and listened, "we offer our deep, sincere apology."
The policy of inflating army kill numbers with civilian deaths included rewards for soldiers such as days of leave and decorations.
In July, defence minister Ivan Velasquez apologised for one of these killings and on Tuesday President Gustavo Petro called the policy tantamount to genocide.
"May rifles never again point at our people," the president said.
Colombia's military fought leftist rebel groups for decades starting in the 1960s until reaching an historic agreement with the main one, known as FARC, in 2016.