Prime Minister Benjamin Netanyahu called the firebombing "an act of terrorism in every respect" and made a rare telephone call to Palestinian president Mahmud Abbas.
But the Palestine Liberation Organisation said it held his government "fully responsible".
The death of 18-month-old Ali Saad Dawabsha was "a direct consequence of decades of impunity given by the Israeli government to settler terrorism", the PLO said.
Abbas said he had ordered his foreign minister to file a complaint at the International Criminal Court in The Hague.
"We want true justice, but I doubt that Israel will provide that," he said of the attack in Duma, near the northern city of Nablus.
The US State Department condemned the "vicious terrorist attack" in "the strongest possible terms," urging Israel to "apprehend the murderers" and calling on both sides to "avoid escalating tensions".
But as protests spread following weekly prayers in West Bank mosques, the Israeli army said troops shot and wounded a protester during clashes in the city of Hebron.
In another sign of a possible flare-up in violence, Palestinians said a youth was moderately wounded by live fire in a clash near Ramallah.
Several thousand people took to Duma's streets for the funeral of the child, whose body was wrapped in a Palestinian flag.
- 'Revenge' sprayed on wall -
The family's small brick and cement home 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 security officials said four suspected settlers set fire to the house before dawn and fled to a nearby Jewish settlement.
The masked assailants reportedly hurled Molotov cocktails through the windows, which were left open because of the summer heat.
Palestinian sources said the injured included the toddler's mother Riham, 26, and father, Saad, as well as his four-year-old brother Ahmed.
The mother was in critical condition with third-degree burns over 90 percent of her body, an Israeli doctor told public radio.
The identity of the fourth person hurt was not immediately clear.
In his call to Abbas, Netanyahu said "everyone in Israel was shocked by the reprehensible terrorism against the Dawabsha family.
"We must fight terrorism together, regardless of which side it comes from," his office quoted him as saying.
- 'Despicable murder' -
Both Netanyahu and President Reuven Rivlin visited the Israeli hospital where the family were fighting for their lives, while Israel's chief rabbi, David Lau, said "all Jews condemn this despicable murder".
The European Union called on Israel to show "zero tolerance" for settler violence, while Jordan, the only Arab state apart from Egypt to have signed a peace accord with Israel, strongly condemned the attack.
"This ugly crime could have been avoided if the Israeli government had not ignored the rights of the Palestinian people and turned its back on peace," government spokesman Mohammed Momani said.
And UN chief Ban Ki-moon condemned the murder while calling on both sides to "take bold steps to return to the path of peace."
For years, extreme-right Israelis have committed acts of vandalism and violence against Palestinians and Arab Israelis, attacked Christian and Muslim places of worship and even Israeli soldiers.
Such attacks rarely lead to convictions.
Vowing revenge, the Palestinian Islamist movement Hamas said the attack "makes the occupier's soldiers and settlers legitimate targets everywhere".
Israeli authorities mobilised a large deployment in Jerusalem's Old City around the flashpoint Al-Aqsa mosque and barred men under 50 years old from entering.
The arson attack follows 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.
Netanyahu holds only a one-seat majority in parliament and settler groups wield significant influence in his government.
West Bank settlements are viewed as illegal under international law, but not by the Israeli government.
They are also major impediments to peace negotiations with the Palestinians, who see the land as part of a future independent state, and Western nations have urged Israel to halt construction.
In other developments, a Palestinian man was killed and another wounded by Israeli fire when they approached a security fence separating the Gaza Strip from Israel, medics said.
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But the Palestine Liberation Organisation said it held his government "fully responsible".
The death of 18-month-old Ali Saad Dawabsha was "a direct consequence of decades of impunity given by the Israeli government to settler terrorism", the PLO said.
Abbas said he had ordered his foreign minister to file a complaint at the International Criminal Court in The Hague.
"We want true justice, but I doubt that Israel will provide that," he said of the attack in Duma, near the northern city of Nablus.
The US State Department condemned the "vicious terrorist attack" in "the strongest possible terms," urging Israel to "apprehend the murderers" and calling on both sides to "avoid escalating tensions".
But as protests spread following weekly prayers in West Bank mosques, the Israeli army said troops shot and wounded a protester during clashes in the city of Hebron.
In another sign of a possible flare-up in violence, Palestinians said a youth was moderately wounded by live fire in a clash near Ramallah.
Several thousand people took to Duma's streets for the funeral of the child, whose body was wrapped in a Palestinian flag.
- 'Revenge' sprayed on wall -
The family's small brick and cement home 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 security officials said four suspected settlers set fire to the house before dawn and fled to a nearby Jewish settlement.
The masked assailants reportedly hurled Molotov cocktails through the windows, which were left open because of the summer heat.
Palestinian sources said the injured included the toddler's mother Riham, 26, and father, Saad, as well as his four-year-old brother Ahmed.
The mother was in critical condition with third-degree burns over 90 percent of her body, an Israeli doctor told public radio.
The identity of the fourth person hurt was not immediately clear.
In his call to Abbas, Netanyahu said "everyone in Israel was shocked by the reprehensible terrorism against the Dawabsha family.
"We must fight terrorism together, regardless of which side it comes from," his office quoted him as saying.
- 'Despicable murder' -
Both Netanyahu and President Reuven Rivlin visited the Israeli hospital where the family were fighting for their lives, while Israel's chief rabbi, David Lau, said "all Jews condemn this despicable murder".
The European Union called on Israel to show "zero tolerance" for settler violence, while Jordan, the only Arab state apart from Egypt to have signed a peace accord with Israel, strongly condemned the attack.
"This ugly crime could have been avoided if the Israeli government had not ignored the rights of the Palestinian people and turned its back on peace," government spokesman Mohammed Momani said.
And UN chief Ban Ki-moon condemned the murder while calling on both sides to "take bold steps to return to the path of peace."
For years, extreme-right Israelis have committed acts of vandalism and violence against Palestinians and Arab Israelis, attacked Christian and Muslim places of worship and even Israeli soldiers.
Such attacks rarely lead to convictions.
Vowing revenge, the Palestinian Islamist movement Hamas said the attack "makes the occupier's soldiers and settlers legitimate targets everywhere".
Israeli authorities mobilised a large deployment in Jerusalem's Old City around the flashpoint Al-Aqsa mosque and barred men under 50 years old from entering.
The arson attack follows 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.
Netanyahu holds only a one-seat majority in parliament and settler groups wield significant influence in his government.
West Bank settlements are viewed as illegal under international law, but not by the Israeli government.
They are also major impediments to peace negotiations with the Palestinians, who see the land as part of a future independent state, and Western nations have urged Israel to halt construction.
In other developments, a Palestinian man was killed and another wounded by Israeli fire when they approached a security fence separating the Gaza Strip from Israel, medics said.
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