Benjamin Netanyahu, the Israeli Prime Minister, immediately accused Yasser Arafat, the Palestinian leader, of giving the "green light" for the resumption of violence. The bombing, the first for over a year, was claimed by Hamas, the Islamic militant organisation.
The explosion took place as people sat down to lunch in the courtyard of the Apropos Coffee House, on Ben Gurion Boulevard, in the centre of Tel Aviv. A man entered carrying two bags. "He looked strange," said Gad Ben Tzur, a waiter.
"I was trying to pick up an order. A second later, there was a tremendous flash and he blew up."
Among the injured were children in fancy dress who were celebrating the Jewish settlement of Purim. A six-month-old baby dressed in a red and blue clown's uniform was taken away covered in blood. The two bags carried by the bomber, in keeping with previous attacks, contained ball bearings and nails, in order to kill and wound as many people as possible.
The suicide bombing came four days after Israel started to build a Jewish settlement at Har Homa in east Jerusalem on land which was captured in 1967. Asked if the building of the settlement might have led to the attack, Mr Netanyahu said: "I find that line of questioning obnoxious and immoral."
The new settlement and the bombing together make it unlikely that Israel will end its occupation of the West Bank as intended under the interim agreement of 1995.
Soon after the bombing, Hamed Bitani, a Hamas leader, addressing a crowd of 10,000 in Nablus, the largest city of the West Bank, said: "I have good news for you. There is a suicide operation in Tel Aviv." As the crowd reportedly cheered, Mr Bitani continued: "This is the only language the occupiers understand, the language of martyrdom."
Israel closed off the West Bank immediately after the attack. Identity papers found near the remains of the bomber suggest that he comes from Zurif village, near Hebron, which is under Israeli security control.
Even before the attack, Palestinian politicians said that because of their inability to stop Har Homa their moderate methods might be replaced by violence. Faisal Husseini, the Palestinian leader in Jerusalem, who had spent the night in a tent at a peace camp he has established on a hill near where Israeli bulldozers are breaking ground for the settlement for 27,000 Jews, said: "People are really convinced that the Israelis are not listening to us. So they may say to us: `Thank you, but stand aside.'"
Salah al-Taamari, a member of the Palestinian Legislative Council, said: "Israel fired a bullet into the peace process. They want us to declare it dead. Let them give it the death certificate."
In Hebron, the Palestinian city from which Israeli forces partially withdrew in January, there was confrontation but also co-operation between Israelis and Palestinians. In the morning some 500 boys attacked Israeli troops with stones in the centre of the city. Troops fired back with rubber bullets and and a particularly toxic tear gas, which led to some 30 rioters being taken to hospital. The demonstrators drove the troops, who appear to have been under strict orders not to use live rounds, 100 yards into the Israeli- held zone and cut off 13 Israeli soldiers in a house.
Jibril Rajoub, the head of Palestinian Preventive Security, whose headquarters is in Hebron, ended the riot by ordering hundreds of his men in and out of uniform to drive back the rioters. Linking arms they marched down the street, shouting: "Go home, boys." A unit of Palestinian soldiers were showered with stones by a Palestinian crowd as they clambered through the window of a building to evict stone throwers who were attacking Israeli troops. The Israeli soldiers, for their part, wrestled an M-16 rifle away from a policeman who was about to open fire.
Local people said they were angry about Har Homa. Shams Edin, 35, a restaurant owner, said: "It is as if you went to drink a glass of water and somebody spits in it." Nevertheless, an opinion poll this week by the Centre for Palestinian Research and Studies, showed that only 9 per cent of Palestinians approved of taking armed action in response to the settlement.
The problem for Mr Netanyahu is that if he wants to stop further suicide bombings he needs the co-operation of the Palestinian security services. He defeated the previous Israeli government in the election last May after four suicide bombings, three by Hamas and one by Islamic Jihad. Two bombs were on board different Number 18 buses on Jaffa Road in Jerusalem and exploded a week apart. The last bomb was at the Dizengoff centre in Tel Aviv, a few streets away from yesterday's attack. It left 13 dead.
Mr Netanyahu accuses Mr Arafat of releasing Hamas members and leaders in recent weeks and therefore giving his tacit assent for the resumption of suicide attacks. He said in an interview in the daily Ma'ariv yesterday: "When the PA [Palestinian Authority] opens its prison gates and releases the leaders of terrorists who declare their intent to renew attacks - it is clear we will view the PA as responsible for these attacks."
But if Mr Arafat does to return to the policy of the "iron fist" against Hamas, which means imprisonement without trial, and torture, he will expect Mr Netanyahu to abide by the terms of the Oslo agreement.