The children's grandmother described a fight between the couple on December 5, which forced the woman to flee their home, leaving behind three children.
"She returned the next day to find two children missing," she said. "We searched the neighbourhood with no success and advised them to report the matter to the police."
She further alleged that the father was not willing to provide for the children, claiming they were from the wife's first marriage.
Police also recovered bloodstained clothes from the scene, suggesting the children were brutally killed before being buried.
"Preliminary evidence indicates murder, with both parents implicated in some way," Kiogora said. "Following the investigation, the law will ensure justice for the children."