The arson attack on 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 curb violence by hardline Jewish settlers.

The child's father, Saad, had been being treated for third-degree burns at an Israeli hospital, where a spokeswoman last week described his condition as "critical".

Early Saturday Ghassan Daghlas, a Palestinian Authority official for the north of the West Bank which includes the village of Duma where the Dawabsha family lived, announced the father had succumbed to his injuries.

"Saad Dawabsha died and plans are underway for his funeral in Nablus," Daghlas said, AFP reported.

The Dawabsha family in Duma also confirmed the death.

Mother Riham and four-year-old son Ahmed were also in an Israeli hospital, where a spokeswoman described their condition last week as life-threatening.

The family's small brick and cement home in Duma was gutted by fire early on July 31, and a Jewish Star of David spray-painted on a wall along with the words "revenge" and "long live the Messiah".

Israel this week used a controversial form of detention without trial normally invoked for Palestinians against an alleged Jewish extremist, following an outcry over the attack.