They say he is probably still armed and could be dangerous though, so are not recommending he be approached.
Fears are increasing that the 35-year-old man, who moved to Germany from Iraq in 2008, may try to leave the country, despite the presence of his wife and other children in Lower Saxony.
Detectives said he may have planned to shoot his daughter Souzan, as he showed up to a meeting with her and youth care authorities in the town of Stolzenau with a gun.
Souzan had moved out of the family home with the help of authorities some time ago due to family disputes. She was killed just after an attempt at reconciliation attempt between her and her family failed. When they walked outside following the meeting, the father opened fire at her in front of the rest of the family.
Souza was hit in the head at least once and died at the scene, slumped against a car in the street.
Detectives have spoken to her mother who is said to have witnessed the killing, but she told them she didn't know where her husband is.
On Tuesday police found a car he is thought to have used to drive away from the scene, and searched some flats nearby, but found nothing of use.