NABLUS: The father of a Palestinian toddler killed last week after their home was firebombed by Jewish extremists has died of his injuries in an Israeli hospital, a Palestinian official confirmed Saturday.

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 sleeping toddler was burned to death when the assailants set fire to two Palestinian homes early on Friday, also critically wounding the child's 4-year-old brother and parents.

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 on 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.

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.

Read Palestine toddler burned to death by Jewish settlers

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.

Israel Prime Minister Benjamin Netanyahu condemned the attack as "terrorism in every respect", and vowed to spare no effort in bringing the perpetrators to justice.

The US administration also condemned the arson attack by branding it a "vicious terrorist" act that must be punished.

In a statement issued on Friday, the US State Department welcomed Israeli Prime Minister Benjamin Netanyahu's condemnation of the attack and called for Israeli authorities to arrest the perpetrators and bring them to justice. It also urged all sides to maintain calm and not escalate tensions.