The explosion on Tuesday hit a shopping centre shortly before 7pm in Netanya, 12km from the West Bank, and Israel sealed the West Bank and Gaza early on Wednesday.
Channel 10 television, quoting Israeli police, said three people were killed in the blast in Israel. Israeli sources said at least 30 people were wounded.
"We heard an explosion, people began to scream and ran to the other exit of the mall," Laura, a shop assistant at the Kenyon Hasharon mall, told Israeli army radio.
Islamic Jihad claim
Al-Quds Brigades, linked to the Palestinian resistance group Islamic Jihad, claimed responsibility for the attack, reported Aljazeera.
Israeli police and Palestinian security identified the bomber as Ahmad Sami Abu Khalil, an 18-year-old member of Islamic Jihad.
Aljazeera correspondent Walid al-Umari said the bomber came from Atil town, north of Tulkarim.
In a statement after the attack, Islamic Jihad said it remained committed to an unofficial ceasefire agreed to in February this year, but reserved the right to retaliate for Israeli violations, such as arrests of the resistance group's members.
In Ram Allah, Palestinian President Mahmoud Abbas condemned as "idiotic" the bombing and said those behind it would be punished.
"This was a crime against the Palestinian people and those who were behind it must be working against our people's interest and must be punished," Abbas said.
"This was a crime against the Palestinian people and those who were behind it must be working against our people's interest and must be punished... Those behind it were behaving idiotically"
"Those behind it were behaving idiotically. There is no rational Palestinian who can conduct such an act at the time Israel was withdrawing from ... settlements starting in Gaza and moving to the West Bank," he said, referring to upcoming Israeli withdrawal from occupied land Palestinians want for a state.
Chief Palestinian negotiator Saeb Erikat condemned the bombing. "We understand that those who carried out this attack want to sabotage the efforts being exerted to have a smooth and peaceful disengagement from Gaza and a revival of the peace process," he said.
A source close to Israeli Prime Minister Ariel Sharon said the latest attack was proof that the Palestinian Authority was "doing nothing to stop terrorism".
Israeli soldiers who swept into Tulkarim early on Wednesday fired into the air and then at a Palestinian police post in what witnesses called an unprovoked attack.
The military also closed off the West Bank and Gaza Strip, banning Palestinians from entering Israel, in response to the bombing.