The explosion turned the green Egged number 14 bus into a charred skeleton at a busy intersection near the Inbal Hotel, where leaders of major US Jewish organisations were meeting.
In a statement sent to Aljazeera, Al-Aqsa Martyrs Brigades -an armed offshoot of Yasir Arafat's Fath movement - claimed responsibility for the bombing.
The statement said the executor of the operation was Muhammad Khalil Zaal, 23, from Husan village in Bethlehem.
"The operation came as retaliation to Shijiyah and Rafah massacres in which 15 Palestinians were killed," said the statement.
Police confirmed the attack was a "suicide bombing".
"People were screaming 'mommy, daddy'. There were body parts everywhere including some hands and feet scattered outside the bus."
"It is a suicide bombing, that is for sure," police spokesman Gil Kleinman told reporters.
A spokesman for the Magen David Adom, the Israeli equivalent of the Red Cross, said at least 62 people were wounded in the blast on a packed number 14 bus near the King David Hotel. Eleven were critically wounded, 14 badly hurt and 29 lightly
injured, he said.
Ambulances raced to the scene. "People were screaming 'mommy, daddy'. There were body parts everywhere including some hands and feet scattered outside the bus," medic Reuven Pohl said. Weeping pedestrians streamed from the scene.
A Palestinian bomber last struck in Jerusalem on 29 January, killing 11 people on a bus.
Quick to respond, the Palestinian Authority condemned the blast and urged the United States to step up peace efforts.
A copy of al-Aqsa Brigades'
statement sent to Aljazeera
"We condemn this attack and we urge ... especially the United States, to step up its efforts and revive the peace process because this is the only way to break this vicious cycle," Saib Uraiqkat, Palestinian cabinet minister told reporters.
The blast came the day before the world court in The Hague is due to begin debating the legality of the barrier along the West Bank, which Israel says it is building to keep out Palestinian armed fighters.
"This attack in Jerusalem is a grim reminder of Israel's need for a security fence to stop such terror in its tracks," said an official from Israeli Prime Minister Ariel Sharon's office.
Israeli Foreign Minister Silvan Shalom said the blast justified the construction of the "separation fence".
"This attack shows that the construction of the security fence is indispensable. Where there is no fence: it is horrible. Where the fence has been built, results are clear cut," said Shalom on military radio. "That is why we will go on building this fence because it saves lives," he added.
Palestinian Prime Minister Ahmad Quraya condemned the attack, making it plain the timing could not have been worse for the Palestinian case against the barrier.
Israel has said Jerusalem blast
justifies the building of the wall
"The Palestinian government stresses that its foremost national interest demands that such acts stop as they serve as excuses for Israel to continue building its wall, carry out its assassinations, raids and targeting of Palestinian civilians," a statement released by his office said.
Minutes before the blast, Israeli work crews began tearing
down an eight km-long section of the West Bank barrier that
separated a Palestinian village from the rest of the territory.