He said the operation was carried out to clear the areas of Taliban.
He said two of those killed are civilians while it is not known whether the four others are residents of the area or militants.
The operation was carried out early on Saturday morning and was supported by the Special Forces as well as the Air Force.
He said that at least 15 suspects, all residents of the villages, were arrested by the Special Unit of the National Directorate of Security during the operation.
Meanwhile, a police commander in Parwan claimed that the operation was not coordinated with them.
Reports indicate that the Kabul-Balk highway which passes through Charikar city in Parwan was closed for few hours by residents of the province to protest civilian casualties in the operation.
Civilian Casualties in First Quarter of 2019
The UN Assistance Mission in Afghanistan said in a report on April 24 that it has documented high levels of harm to civilians but adds that there has been a 23 percent decrease in overall civilian casualties as compared to the same period last year and is the lowest for a first quarter since 2013.
The report says the UN documented 1,773 civilian casualties (581 deaths and 1,192 injured), including 582 child casualties (150 deaths and 432 injured) between January 1 and March 31.
In the first quarter of 2018, UNAMA documented 2,305 civilian casualties (799 deaths and 1,506 injured), including 609 child casualties (176 deaths and 433 injured), the report says.
The overall reduction of civilian casualties was dr