A police spokesman confirmed on Wednesday that the 69-year-old had put the one-year-old girl in a baby hatch at a nearby hospital at the weekend.
He then killed his 28-year-old wife and their boys aged three and six, and then waited some time before killing himself.
They died several days before neighbours raised the alarm on Tuesday evening.
“This was a family tragedy,” said police spokesman Stefan Redlich. “We think the family was very heavily in debt.”
An open window at the family's two-storey home in the Gatow area of Spandau raised the suspicions of neighbours in the respectable area, and they also noticed that the car had not been moved for several days.
“There is nothing to indicate that the woman wanted the killings,” said Redlich. He said the victims had not been shot, but a cause of death was not available on Wednesday.
Police on Wednesday appealed for help in tracking down another man suspected of having killed his family, releasing Fallah Sänger's name and picture two days after they say he shot dead his wife and their two children.
Details have emerged that he was known to the police for beating up his wife, and although they had split up previously, he was living in the flat with the family at the time.