Questions have been asked as to how Mr Fritzl could keep the cellar a secret
DNA evidence supports an Austrian man's confession that he fathered six children by his daughter while keeping her prisoner for 24 years, police say.
Lower Austria police chief Franz Polzer said Josef Fritzl, 73, had completely deceived his wife, his family and the authorities in the town of Amstetten.
Hospital officials meanwhile said Mr Fritzl's daughter and her children had experienced an "astonishing" reunion.
They met at the clinic where they are receiving psychiatric treatment.
Earlier, Mr Fritzl was detained for a further 14 days by a regional court in the provincial capital of St Poelten. On the advice of his lawyer, he did not speak to the examining magistrate.
His lawyer told the BBC that although Mr Fritzl showed no signs of remorse, he looked very sad and "emotionally broken".
Speaking at a news conference in Amstetten afterwards, the director of the psychiatric clinic at a local hospital said Fritzl's daughter Elizabeth, now 42, had been reunited with five of her six children and her mother there on Sunday morning.
KEY FACTS IN CASE
Elisabeth reappeared at home after disappearing 24 years ago
Six children she says are hers have been found and placed in care
One of the children, aged 19, is seriously ill in hospital
Elisabeth's father Josef Fritzl, 73, has been arrested on suspicion of incest and abduction
Police say Mr Fritzl confesses to imprisoning Elisabeth and fathering her seven children
"It was astonishing how easily it happened - how the mother and grandmother came together," Berthold Kepplinger said.
Three of the children were kept in the cellar with their mother and had never seen daylight. The other three were adopted or fostered by Mr Fritzl, after he forced Elisabeth to write letters saying she could not look after them.
The eldest, 19-year-old Kerstin, became seriously ill earlier this month and had to be taken to hospital, where she is currently in a coma. She was imprisoned by Mr Fritzl along with her 18- and five-year-old brothers.
Police have said there is no evidence to suggest the grandmother, Rosemarie, nor any of the seven children she had with Mr Fritzl, were aware of any of the alleged crimes.
Mr Kepplinger said the family members had interacted very naturally, although he said two of the children who had spent their lives underground had a way of communicating that was "anything but normal".
"The children are quite well, they are under investigation, there is a professional team consisting of psychiatrists, neurologists, psychotherapists, speech therapists, physiotherapists, a whole team is working on this," he said.
"One important thing is not to over-treat them."
Mr Kepplinger said Elisabeth had spoken "quite a lot" about what she had gone through in captivity, but declined to provide details.
"It was definitely dreadful for her and for her children," he added.
Speaking at the same news conference, police officials said their investigations and genetic evidence gathered since Sunday had confirmed statements made by Elisabeth and Mr Fritzl's confession.
"The DNA tests provided decisive evidence that the six children that Elisabeth gave birth to have the same father," Franz Polzer said.
Police chief on Austrian case
Mr Polzer said that letters which Mr Fritzl had forced Elisabeth to write had played an important part in deceiving his family and the authorities since her disappearance in 1984, when he allegedly lured her into the cellar of their house and locked her up.
The first letter said Elisabeth had run away, joined a religious sect and asked police not to look for her. Others explained why she had left three of the children on the doorstep of the family home over the years.
Mr Polzer said the last two letters Elisabeth was forced to write had provided considerable evidence to confirm her allegations. The second to last was found in the clothes of Kerstin, when she was admitted to hospital on 19 April.
Mr Fritzl also had another letter with him, Mr Polzer said, where his daughter raises the possibility of returning to the family, bringing with her two sons, aged 18 and five years old.
Mr Polzer said Mr Fritzl had shown the last letter to police as evidence that he did not know about his daughter's whereabouts.
He looks very sad. It is like he is emotionally broken
Rudolf Mayer Mr Fritzl's lawyer
"The biological tests show clearly that this letter, a normal letter with a stamp, was without doubt created by one Josef Fritzl," he added.
"You can be sure that this man left nothing undone in order to deceive the family, his wife, the relatives, the children and everybody around him," he added. "He had no scruples to use every possible means to deceive the public and cover up his crime."
Mr Polzer said official records showed that Mr Fritzl had no criminal convictions from the past 15 years and that the statute of limitations would apply to any earlier offences he may have committed.
Police investigations at the house are meanwhile continuing. The cellar where Elisabeth and three of her children were held captive is being searched inch by inch, in addition to the upstairs flat.
Prosecutors have said Mr Fritzl faces up to 15 years in prison if he is eventually convicted on charges of raping and beating his daughter, and sequestration.
Natascha Kampusch's concern for victims
They are also considering charges of "murder through failure to act" in connection with the death of one of the seven children he fathered. Police said on Monday that Mr Fritzl had admitted burning the infant's body shortly after it died.
Asked whether Mr Fritzl would plead guilty to any of the charges, his lawyer, Rudolf Mayer, told the BBC's Europe Today programme:
"He had made... a confession, but I will speak to him about whether this is right or not."
Mr Mayer said his client had not shown any remorse for what he is accused of doing.
"I can tell you that no sympathy is there at all. The print mediums and all the televisions in Austria write that he is a monster, and no sympathy, nothing."
"He looks very sad. It is like he is emotionally broken," he said, adding that his client was receiving psychiatric care in prison.
The BBC's Bethany Bell says the case is reminiscent of that of Natascha Kampusch, the Austrian teenager held captive in a cellar in a house in a Vienna suburb for eight years, who ran to freedom in 2006.
On Monday, Ms Kampusch, now 20, told reporters that she wanted to contact Elisabeth to offer emotional and financial help.
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