Hamas, which took control of the Palestinian legislature 2½ weeks ago following its election victory, defended Monday's attack — claimed by a separate Islamic militant group as a legitimate response to Israeli "aggression."
Islamic Jihad took responsibility for the bombing.
The body count and toll of wounded was relatively low because the bomber was stopped by a security guard before he could enter the restaurant, CBS News correspondent Allen Pizzey reports.
Hamas has been abiding by a cease-fire signed a year ago, but at the same time it says it will do nothing to halt attacks by militants against Israel.
Pizzey reports that the attack was touted as retaliation for Israeli shelling of areas in the Gaza strip used to fire rockets into Israel — a tactic the Israeli Prime Minister Ehud Olmert, who took office on Monday, says will continue as long as rockets keep being fired at his citizens.
Palestinian officials say Israeli aircraft have fired missiles into a Gaza City metal workshop. The Israeli army says militants had been making homemade rockets there. Palestinians say no one was injured.
The air strike came hours after the Palestinian bomber blew himself up in Tel Aviv.
The moderate Palestinian president, Mahmoud Abbas of the rival Fatah party, condemned the bombing and said he had ordered Palestinian security forces to prevent future attacks.
"These kinds of attacks harm the Palestinian interest, and we as an authority and government must move to stop it," Abbas said. "We will not stop pursuing anyone who carries out such attacks."
But because the increasingly powerful Hamas characterized it as "resistance," the attack may well be the beginning of a new round of blood in the streets, Pizzey reports.
The blast went off at about 1:40 p.m. outside the packed "The Mayor's Felafel" restaurant in Tel Aviv's Neve Shaanan district. The restaurant is in the bustling Neve Shaanan neighborhood near Tel Aviv's central bus station which was crowded with holiday travelers.
A witness, Israel Yaakov, said the blast killed a woman standing near her husband and children, who were slightly wounded.
"The father was traumatized; he went into shock. He ran to the children to gather them up and the children were screaming, 'Mom! Mom!' and she wasn't answering, she was dead already ... it's a shocking scene."
In other developments: