The children were found in a private apartment in the city of Solingen in
North Rhine-Westphalia state, police told AFP without giving further details.
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They were one, two, three, six and eight years old, according to a report in the Bild daily.
The mother later threw herself in front of a train but survived with serious injuries, the report said. She has been taken under police protection.
According to Bild, the children's grandmother called the police and reported that her daughter, 27, had killed five of her children and was possibly on the run with another child with the intention of killing herself.
The woman's 11-year-old son was later found unharmed, it said.
The mother later travelled to the main station in Düsseldorf, some 35 kilometres away, where she jumped in front of a train, according to Bild.
She was rescued from between two track beds and taken to a local hospital
for treatment, national news agency DPA reported, citing emergency services.
Investigations are ongoing, police said.