Six people were injured in the attack, which was carried out on Monday evening by as many as six masked men with automatic weapons in the village of Bilge near the city of Mardin in the Kurdish region of the country.
The Turkish NTV channel reported that the slaughter was part of a blood feud between rival families.
"The prevailing opinion is that the incident was not a terrorist attack. At the same time, prosecutors will thoroughly investigate all scenarios," Atalay said on NTV.
He added that security forces had been deployed to the area and "necessary measures" were being taken.
The interior, justice and rural affairs ministers were to go to the region on Tuesday. Prime Minister Tayip Erdogan took personal control of the investigation.
The Kurdish area of southeastern Turkey has seen 25 years of fighting between separatist guerillas and government troops in which an estimated 40,000 people have died.