The firebombing of the family's home in the occupied West Bank that killed 18-month-old Ali Saad Dawabsha sparked an international outcry over Israel's failure to get to grips with violence by hardline Jewish settlers.
The child's father, Saad, was being treated for third-degree burns at the Soroka hospital in southern Israel, where a spokeswoman described his condition as "critical".
Mother Riham and four-year-old brother Ahmed were being treated at Tel Hashomer hospital near Tel Aviv, where a spokeswoman described their condition as life-threatening.
That was indicative of so-called "price tag" violence -- a euphemism for nationalist-motivated hate crimes by Jewish extremists.
The arson attack followed days of tensions over West Bank settlements, with right-wing groups opposing the demolition of two buildings under construction that the Israeli High Court said were illegal.
The demolition began Wednesday, but Netanyahu the same day authorised the immediate construction of 300 settler homes in the same area, angering Palestinians.
