The firebombing of the family's home in the occupied West Bank, which 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.
His father Saad was being treated for third-degree burns at a hospital in southern occupied lands, 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, AFP reported.
The family's small brick and cement home in the village of Duma was gutted by fire, and a Jewish Star of David spray-painted on a wall along with the words "revenge" and "long live the Messiah."
That was indicative of so-called "price tag" violence - a euphemism for nationalist-motivated hate crimes by Jewish extremists.
Palestinian protesters took to the streets across the West Bank, including Israeli-annexed east Jerusalem, triggering clashes with the Israeli army.
North of Ramallah, troops shot Laith Khaldi, 17. He was pronounced dead early Saturday. The army claimed he had thrown a fire bomb.
On Saturday morning, Palestinians and Jewish settlers clashed near Kusra in the northern West Bank, trading volleys of stones until the Israeli army declared the area a closed military zone.
In east Jerusalem, some 10 Palestinians were wounded in overnight clashes with Israeli police, Palestinian sources said.
On Saturday, two officers were lightly wounded dispersing a riot, police said.
Palestinian President Mahmoud Abbas on Friday ordered his foreign minister to file a complaint at the International Criminal Court in The Hague over the Israeli killing of the toddler.