Fritzl, 73, was formally placed in confinement on April 29.
He had been detained three days earlier on suspicion of locking up his daughter Elisabeth for 24 years and fathering her seven children.
Authorities say Fritzl confessed to locking up his daughter and repeatedly raping her.
Investigators say he also told them three of the children were raised in a cellar at his home in Amstetten, west of the capital Vienna, three others were brought up above ground, and one died in infancy.
DNA tests have confirmed Fritzl is the biological father of the six surviving children.
He is expected to be charged once investigations are completed.
Meanwhile, in Amstetten, detectives have continued to comb through Fritzl's large property for evidence.
Franz Polzer, chief investigator, said his team was making good progress, but it was likely to still take some time before the entire property and its contents were thoroughly examined and analysed.
Polzer said a yard search on Thursday using sniffer dogs had not produced any results.
He said: "We have already come very far. We want to be absolutely sure... this man exercised unbelievable violence."
Fritzl's alleged double life began to fall apart when Elisabeth's oldest child, a 19-year-old woman, was hospitalised with a severe infection.
Unable to find medical records for the woman, doctors appealed for her mother to come forward.
Fritzl accompanied Elisabeth to the hospital on April 26 and was detained after she divulged what had allegedly happened to her.
In comments relayed through his lawyer and published in the Austrian magazine News on Thursday, Fritzl was quoted as saying he knew it was wrong to hold his daughter captive and that he "must have been crazy" for doing so.
He added that he tried to care for her and their children as best as he could by taking them flowers, toys and books.