Bush said "I strongly deplore" Monday's attack, the deadliest suicide bombing in 20 months. Israel held the Hamas-led Palestinian Authority responsible for the attack, but stopped short of ordering a large-scale military operation.
Bush urged restraint, but angrily called on Palestinians to reject violence.
"It is unjust and it is unnecessary," he said. "I have consistently reminded all parties that they must be mindful of whatever actions they take and mindful of the consequences. ... For those who love peace in the Palestinian territories, they must stand up and reject this kind of violence."
United Nations Secretary-General Kofi Annan called Prime Minister Ehud Olmert and condemned the attack.
Meanwhile, Egypt and the Arab League condemned Tuesday the attack in Tel Aviv that killed nine people and called on both sides to return to the negotiation table.
Egyptian Foreign Minister Ahmed Aboul Gheit described the attack as "an act of terrorism," a strong condemnation from an Arab state that usually jointly blames both Israel and the Palestinians for the ongoing violence.
Monday's suicide blast, which killed nine and wounded dozens outside a packed Tel Aviv fast-food restaurant, was carried out by a bomber from the Islamic Jihad group, but leaders from Hamas group now in power have justified it as a response to the Israeli "aggression" against the Palestinians.
The Associated Press contributed to this report