Searches for the four-year-old on land, water and by air have been conducted following the incident but there has yet to be any sign of the missing girl.
PJ police are investigating the circumstances leading up to the mother and her two children being on the beach and in the water on Monday night.
The woman, named by newspaper Correio da Manhã as Sonia Lima, was detained on Wednesday by PJ police on suspicion of murdering her daughters after an arrest warrant was issued by the Public Prosecutor.
The alarm was raised on Monday night by a passing taxi driver who spotted the woman emerging from the water in a panic.
Quoting a source from the Portugal’s Judiciary Police (PJ), newspaper Público reported earlier this week that a complaint regarding the sexual abuse of a child had been made to the authorities but “nothing has been proven.”
The same source told the newspaper that the likeliest scenario is “murder followed by a suicide attempt within the context of a separation, depression and solitude.”
The newspaper claims the young girls “fell into the river with their mother.”
In comments to Público, Joana Garcia da Fonseca, head of the Protection Committee for Children and Youths (CPCJ), elaborated “the complaint related to sexual abuse by the father.”
In a statement released on Wednesday the father vehemently refuted all allegations made against him, saying the press is more focused on “falsehoods made about the life of my family” than the missing girl’s whereabouts.
The family lived in Carenque, Amadora (Lisbon) and had been flagged by authorities for domestic violence, suspicions of which also fell on the children’s father.
Last November the PSP police informed the CPCJ of the situation, who sent the case on to the Public Prosecutor’s Office for judicial proceedings to be launched with a view to protecting the children, and for criminal proceedings to be brought against the suspect.
According to Público no proceedings were launched by the Amadora CPCJ branch as child protection committees no longer have authority to intervene in cases of child sex abuse following alterations to child and youth protection laws last year. Público reports that on 2 December 2015 the Public Prosecutor asked for a judicial case to be opened in order to protect the two children after a complaint was made to the PSP police accompanied by a statement from the Amadora-Sintra Hospital.
An investigation into claims of child sex abuse and domestic violence was launched at the end of November.
It was the girls’ father who went to the Amadora PSP station last Friday (12 February) to report them missing after being unable to get in touch with his wife or find his daughters.
Authorities were dispatched to the Giribita beach in Caxias after being tipped off by a witness, who saw a woman leave a parked car with a child in each arm and head for the sea.
A short while later the woman emerged from the water “in a state of panic and with hypothermia” claiming her children were still in the water, the Commandant of Lisbon Porto told Público.
Speaking to newspaper Correio da Manhã and its TV channel, relatives of the mother said the woman had been living with domestic violence at the hands of her spouse for five years.
The newspaper claims she had started to suspect the man was sexually abusing their eldest daughter last November and left the family home, having moved to an aunt’s house in Vila Franca de Xira.
Family members affirm the woman had lodged complaints with the PSP and GNR police as well as with Social Security and the Association for Victim Support and Protection APAV.