There have been no further interviews with the man since Saturday afternoon, but it has been revealed that the murdered 12 year old was the daughter of the 26 year old man's partner.
The man is also suspected of the attempted murder and rape of his stepdaughter's friend, who managed to escape from the apartment and raise the alarm.
The friend is now being treated in hospital. Her injuries are said to be serious but not life-threatening, and her condition on Sunday morning was unchanged.
On Saturday afternoon the 26 year old met his lawyer, Bo Hegestam, who said that his client neither admitted nor denied the crimes, since he had no memory of the night's incidents.
"He feels very unwell and so it hasn't been possible to hold meaningful interviews with him," said Mats Nylén, information officer at Södertorn police.
According to reports in Aftonbladet and Expressen, the man has for a long time been a user of anabolic steroids and is described as a violent person by police and acquaintances.
Aftonbladet said that the man has at his own request been treated for psychiatric problems and has served time in prison for serious assault.
Mats Nylén declined to comment on whether the man was under the influence of drugs or alcohol during the attack, but said that several blood samples had been taken.
"It's routine with this type of crime and the results are expected within a few days," he said.
Police spent most of Saturday carrying out a forensic examination of the apartment.
"I don't want to say anything about the examination or any possible murder weapon at this stage of the investigation," said Nylén.
On Saturday evening police denied earlier reports that both the girls had been raped by the man.
"But that could change during the course of the inquiry - we will be interviewing several witnesses and are awaiting the forensic results.