“Unknown gunmen broke into a house in the village of Abu Garma and killed a 45-year-old woman and her three children,” who were between 10 and 15 years old, Lieutenant Colonel Ahmed al-Karkhi said.
The attack with silenced weapons probably occurred between 3:00 and 4:00 am (0000 and 0100 GMT) on Friday, he said, adding the bodies were found about 9:00 am (0600 GMT) by a family member.
A police lieutenant colonel involved in the investigation said the attack might have a sectarian motive, and could lead to further violence.
“Most of those killed in the two attacks were Shiite, and the family killed later was Sunni,” he said.
“It seems like a sectarian incident, and there is a risk that it might lead to more sectarian violence in the area.”
Karkhi said a suicide car bombing near a cafe in Abu Garma on Thursday followed by another bombing inside it as the casualties were being carried out killed eight people and wounded 18 others.
Abu Garma is a small village of between 150 and 200 people north of Baquba, the capital of Diyala province. Its centre is mainly Sunni, while its outer areas are mainly Shiite.
The 2006 bombing of the Shiite Al-Askari shrine in Samarra unleashed an orgy of sectarian bombings and death squad murders in which tens of thousands of Iraqis were killed, and many more forced from their homes.
The violence was eventually brought under control when Sunni tribesmen switched sides and began battling militants and the United States sent thousands of additional soldiers.
But while violence is down from its peak in 2006 and 2007, attacks remain common here, killing 112 Iraqis in March, according to government figures.