Officials are also considering charges of "murder through failure to act" which carries a longer sentence, in connection with the death of one of the seven children he fathered.
For Fritzl has admitted to disposing of the body of the newborn in an incinerator shortly after the birth.
His lawyer, Rudolf Mayer, has told the BBC his client will undergo a series of psychiatric and psychological tests.
He says the tests will be crucial in determining the extent of Fritzl's guilt and his penalty.
"This case certainly requires a thorough psychiatric and psychological examination. We need to establish if he can be considered responsible for his actions," Mayer told BBC News.
"We'd need to see if there's evidence of any psychiatric disorder - which wouldn't necessarily mean mental incapacity but would still be very important when assessing the guilt of the suspect. And the extent of the guilt determines the extent of the penalty," he said.
The head of the city's social services, Hans-Heinz Lenze, said officials were also considering changing the names of the immediate family members to give them new identities.
"At the moment, all possibilities are being sounded out in closest consultation with the family," Lenze told a news conference, AFP reports.
Meantime Austrians are rallying around to provide emotional support to the abused Fritzl family.
Overnight on Tuesday, hundreds of people gathered in the town of Amstetten, 75 miles (120km) west of Vienna.
During the gathering - organised by a local convent school - children, their parents, teachers and nuns lit candles and stood in the rain to express their solidarity and outrage.
Officials said Elisabeth, now 42, and two of the three children who had lived with her in the cellar - the 18- and five-year-old brothers - had an "astonishing" reunion with her other children on Tuesday.
The eldest of the cellar children, 19-year-old Kerstin, became seriously ill earlier this month and is in a coma in hospital.
The other children lived an apparently normal life with Fritzl as his "grandchildren" in the upper sections of the same house.
Fritzl's wife, Rosemarie, who was told by her husband that their daughter had run away from home to join a religious cult, also had an emotional meeting with her daughter, officials said.
The three children who lived upstairs were adopted or fostered by Fritzl and his wife, after he forced Elisabeth to write letters saying she could not look after them.
Berthold Kepplinger, director of the psychiatric clinic, said the family members had interacted very naturally, although he said the two children who had spent their lives underground, without seeing daylight, had a way of communicating that was "anything but normal".
He said Elisabeth had spoken "quite a lot" about what she had gone through in captivity, but he declined to provide details.
Lower Austria police chief Franz Polzer said the 73-year-old, had completely deceived his wife, his family and authorities.
Police have said there was no evidence to suggest the Mrs Fritzl, nor any of the children she had with Fritzl, were aware of any of the alleged crimes.
The case in the eastern Austrian town of Amstetten has prompted inevitable comparisons with that of Natascha Kampusch, held captive in the cellar of a house near Vienna for eight years until her escape in 2006. And many Austrians are extremely embarrassed.
But Chancellor Alfred Gusenbauer said he planned to launch an image campaign to restore the country's reputation abroad.
Speaking from Vienna, he underlined that the "abominable events" were linked to one individual case.
"We won't allow the whole country to be held hostage by one man," he said, adding: "It's not Austria that is the perpetrator.
"This is an unfathomable criminal case, but also an isolated case," he stressed.