Police said around 60 people were wounded in the blast, which turned the green number 14 bus into a charred skeleton at a busy intersection near the Inbal Hotel, where leaders of major US Jewish organisations were meeting.
"People were screaming 'mommy, daddy'. There were body parts everywhere including some hands and feet scattered outside the bus," medic Reuven Pohl said.
The World Court begins hearings in The Hague on Monday on the legality of the West Bank barrier that Israel says keeps suicide bombers out, but which Palestinians call a land grab.
Al-Aqsa Martyrs Brigades claimed responsibility for the bombing and released a farewell video showing the bomber seated in front of the group's flag.
In a statement it called the barrier "a Nazi wall which will not stop us attacking".
It later issued a "clarification" denying involvement in the bombing, which it said only served Israeli propaganda interests.
It did not explain why it had issued the earlier statement or the video.
Arafat's office condemned the bombing and called the timing deliberate and harmful for the diplomatic campaign against the barrier. The top Palestinian security body vowed to bring those responsible to justice.
When one Israeli minister suggested at Sunday's cabinet meeting that the attack could be seen as a protest against the barrier, Prime Minister Ariel Sharon said: "We don't have to look for a reason why Jews are killed and they won't stop killing Jews ever."
The bomber struck during the morning rush hour at the start of the Israeli work week. Police said the bomb was packed with metal shards to make it more deadly.
"The Palestinian murderers have again shown that Israel is not the aggressor, the Palestinians are, and that the fence was not meant for anything other than to save lives," Justice Minister Yosef Lapid said.
"I hope that the 15 justices in The Hague understand the message.... If there was a fence around Jerusalem there would not have been an attack today."
FAREWELL VIDEO: Al-Aqsa named the bomber as Mohammed Zaal, a 23-year-old from Hussan village near the West Bank town of Bethlehem. It said the attack was a reaction to the barrier and to an Israeli raid that killed 15 Palestinians in Gaza City on February 11.
In the farewell video, the bomber read a statement that warned Israelis "the more your army attacks our people, the more martyrdom operations there will be".
Israeli troops sealed off Bethlehem after the attack. A Palestinian security official said soldiers arrested the bomber's wife, mother, father and four brothers.
Initially Israeli officials said seven people were killed in the blast, but forensics experts later detected the remains of an eighth victim, police said.
One of those killed was the brother-in-law of an Israeli diplomat serving in The Hague, an Israeli official said.
Palestinian groups have killed 867 Israelis during more than three years of conflict. At least 2,350 Palestinians have been killed since the uprising began in 2000.
A Palestinian suicide bomber last struck in Jerusalem on January 29, killing 11 people on a number 19 bus. Israel has sent the wreckage of that vehicle to The Hague as part of its public relations offensive for the World Court hearings.
About 180 km of the planned 730 km West Bank barrier has been built.
Minutes before the blast, Israeli work crews began tearing down an eight km-long section of the barrier that separated a Palestinian village from the rest of the West Bank. Construction continues elsewhere, including near Jerusalem.
Palestinians call the barrier an attempt to seal a hold on land Israel has occupied since the 1967 Middle East war.
The Hague court will issue a non-binding opinion on the barrier at the request of the United Nations. Israel has made a written submission, but will not attend the proceedings, leaving campaigners to put its case outside the court.
Relatives of suicide bombing victims, who flew to the Netherlands to defend the barrier, confronted Israeli Arab lawmakers who were there to support the Palestinian case.
"Child killers, child killers," they chanted at the airport baggage carousel as Dutch police watched nervously.