A half-hour after the bombing, Israeli helicopter gunships fired missiles at a car in a crowded neighborhood of Gaza City, killing two Hamas militants and five bystanders and wounding 30 other people. Another two militants were killed in a separate helicopter strike hours later.
The attacks threatened to sweep away a new Middle East peace initiative in a wave of violence.
The first two attacks unfolded in such rapid succession that the scenes of carnage played out nearly simultaneously in Jerusalem and Gaza. Israelis and Palestinians watched televised images from both cities of rescue crews carrying victims on stretchers, screaming ambulances ferrying the wounded, vehicles mangled by explosives and streets strewn with debris and body parts.
After a period of hesitant hope raised by the launch of the new peace plan at a Middle East summit last week in Jordan, there was renewed fear on both sides of the conflict that Israelis and Palestinians were once again descending into a maelstrom of bloodshed.
President Bush, distressed by the latest assault on the "road map" peace plan that he has vigorously promoted in recent weeks, called for international action to stop the killing.
"To the people in the world who want to see peace in the Middle East, I strongly urge all of you to fight off terror, to cut off money to organizations such as Hamas, to isolate those who hate so much that they're willing to kill to stop peace from going forward," Bush said after he condemned the Jerusalem bombing, which was claimed by Hamas.
Palestinian leader Yasser Arafat and Prime Minister Mahmoud Abbas called for an immediate halt to militant attacks, but Dr. Abdel Aziz Rantisi, the Hamas leader targeted Tuesday, said the attacks would continue. Israeli Prime Minister Ariel Sharon pledged to press on with strikes against the militants.
In a televised statement, Arafat said: "The hellish cycle of terrorist operations by all sides must stop now, and immediately. I strongly condemn the terrorist operation that targeted Israeli civilians in Jerusalem today, and I condemn just as strongly the Israeli terrorist operation that attempted to assassinate brother Dr. Abdel Aziz Rantisi."
A statement issued by Abbas, who has been trying to negotiate a cease-fire with Hamas and other militant Palestinian factions, said that "stopping this deterioration requires all parties to comply with a cease-fire and end violence and start serious efforts to implement the road map."
Omar Suleiman, Egypt's intelligence chief, met in Ramallah with Abbas and Arafat in an effort to arrange a truce, but Hamas representatives did not attend.
Rantisi, recovering from Tuesday's attempt on his life, promised more attacks. "Our people will teach the Israeli enemy tough lessons until the Israelis stop their terror and crimes," he said.
Sharon said that while Israel "is deeply committed to make every effort to move forward in the political process," the government will "take all steps to protect the security of the citizens of Israel."
The bombing in Jerusalem blew apart the No. 14 bus as it moved through traffic on Jaffa Road, the city's main street, which has been the scene of several Palestinian attacks. Dressed in the ritual fringed garment worn by Orthodox Jews, the bomber detonated explosives filled with ball bearings shortly after boarding the bus.
The force of the blast peeled off the roof at the front of the bus, flinging some passengers out of the vehicle while killing others in their seats.
"There was an explosion, a horrible boom, and the bus started burning," said Eliahu Shmueli, a city parking inspector who was nearby. "I ran to the bus and saw people on fire. I tried to put them out with my hands. I tried to pull out one woman, but she was caught between the seats. She was still alive, she was on fire. She died in my hands."
Recovery workers removed bodies from the bus in white bags and lined them up on the sidewalk.
At the neighboring Mahane Yehuda market and in nearby Zion Square, police dispersed angry crowds who tried to attack Arab workers.
In Gaza, Hamas militants claimed responsibility for the bombing in loudspeaker announcements, and in the West Bank town of Hebron, members of the group identified the bomber as Abdel Mu'ti Shabana, a local resident.
About a half-hour after the bombing, Israeli helicopter gunships struck in Gaza City, firing missiles at a car carrying two Hamas militants. Witnesses said two missiles hit the vehicle as it stood in traffic, and another landed as people gathered around the car.
Five bystanders were killed along with the militants, one of whom was identified as Tito Masoud, a leader of the armed wing of Hamas. An Israeli security official said he had been involved in the manufacture and firing of homemade Qassam rockets, which have been launched at southern Israel.
After the attack, angry crowds surged around the targeted vehicle as the charred bodies were pulled out. A few hours later, two more militants were killed in another helicopter strike at a car in Gaza. The army said it had struck a Qassam rocket squad on its way to an attack.