Police and medics reached the scene quickly
BBC Middle East analyst Roger Hardy says the attack will strengthen the hand of Mr Sharon against doves in his cabinet who have been pushing for more political dialogue with Palestinian leaders.
A senior adviser to Israeli Prime Minister Ariel Sharon blamed Palestinian leader Yasser Arafat for the bombing.
Dore Gold said Mr Arafat bore responsibility for the attack because he had not put an end to incitement to violence against Israelis.
"Yasser Arafat and the Palestinian Authority are directly responsible for the deaths," he told the BBC.
Mr Arafat condemned the attack and called for a joint ceasefire.
Raanan Gissin, a spokesman for Mr Sharon, refused to reveal how the government planned to react to the attack, but said that "Israel is definitely going to respond."
The sentiments were echoed by Jerusalem Mayor Ehud Olmert.
"We are in a war... We will act together with the government to reach every one of those who is responsible for terror, to hit them and kill them," he said.
In a strongly worded statement, US President George W Bush called on Mr Arafat to "act now to arrest and bring to justice those responsible, and take immediate, sustained action to prevent future terrorist attacks".
Competing claims
Hamas, the hard-line Palestinian militant group, said one of its members had been the bomber.
Islamic Jihad, which had also claimed responsibility, later said it had mistakenly thought that one of its activists was behind the blast.
"Our fighter Hussein Abu Amsha was en route to carry out a martyrdom operation and when the explosion happened, our brothers thought it was him," Islamic Jihad General Secretary Ramadan Shallah said in Damascus.
Palestinian legislative council member Hanan Ashrawi said the pizza parlour attack was part of a cycle of violence.
Palestinian information minister Yasser Abed Rabbo went farther: "Sharon provoked it. Sharon waited for it. Sharon wanted it," he said.
The nail-packed bomb exploded in what Mayor Olmert called one of the busiest intersections in Jewish west Jerusalem at the busiest part of the day.
Shattered glass covered the ground around the Sbarro restaurant in the busy Jaffa Street shopping district.
Dozens of ambulances, sirens blaring, rushed to the scene. Many of the casualties were children.
A doctor at nearby Shaare Zedek hospital said he had three critically injured patients between the ages of four months and a year and a half.
Dozens killed
Palestinian suicide bombers have killed dozens of Israelis since the uprising began after peace talks became deadlocked.
Hamas and Islamic Jihad have claimed responsibility for most of the bombings.
Jerusalem shop-owner Nava Perry saw the aftermath of the blast: "We saw bodies thrown all over the floor and people ran into my store dripping with blood.
"I saw bodies inside the restaurant and the body of a little girl on the street outside full of blood.
"Bodies were all over inside and outside. Sbarro is completely blown up."
The attack came amid high tensions between the Palestinians and Israelis, with Palestinian militants vowing revenge for Israel's policy of killing activists they consider a threat to Israeli security.
"They must understand that the blood of our people is not cheap."
A Palestinian official has warned that growing support among Palestinians for radical Islamist groups is making it harder for the Palestinian Authority to govern the West Bank and Gaza Strip.
In a separate incident on Thursday, an Israeli soldier was shot dead by a Palestinian sniper near the West Bank town of Tulkarm.
Palestinian television reported that Israeli tanks began shelling a Palestinian village in the south of the Gaza Strip shortly after the attack.
Later, a 19-year-old Israeli woman died near an Israeli farming community near the West Bank after coming under fire from Palestinian gunmen.