Emergency services rushed to the scene
"We saw a Palestinian terrorist shoot at us from the outside. He didn't stop shooting," a woman passenger on the bus told Israel radio.
Jerusalem Police Chief Mickey Levy said between one and three gunmen had opened fire on the bus, which was at the French Hill junction in the north of the city.
An Israeli civilian, who identified himself only as Marcus, told the Associated Press he fired on one of the gunmen after he saw him start shooting.
Mr Levy told Israel radio that a border police officer and a soldier shot and killed one of the gunmen.
Two other men were seen running from the scene, though it was not clear if they were involved.
Mr Levy said the dead attacker was a member of the militant group Islamic Jihad, from the West Bank town of Hebron.
Avi Zohar, director of the Magen David Adom ambulance services, said two people on the bus were dead. Four others were seriously injured and more than ten were slightly injured.
Planned troop withdrawal
In a statement, the Palestinian Authority "strongly" condemned the shooting and vowed to bring the guilty parties to justice.
But the statement also blamed Israel for "the deterioration of the situation... due to its continuing occupation of Palestinian autonomous areas and its policy of assassinating Palestinians."
The shooting came just hours after the Israeli Government said it would withdraw its troops from the West Bank town of Qalqilya on Sunday, one of five Palestinian-controlled towns they occupied after the assassination of an Israeli cabinet minister last month.
Foreign Minister Shimon Peres said he did not think the planned withdrawal would be affected by the shooting, saying that Qalqilya itself had been calm in recent days.
Israeli sources have told the BBC there is no timetable to leave the remaining four towns, of Ramallah, Tulkarm, Nablus and Jenin.
News of the planned withdrawal came a few hours after Israeli helicopters launched rocket attacks on Palestinian targets in the Gaza Strip.
Mortar shells
Israel said the attacks were aimed at three buildings which made mortars to be fired into Jewish settlements.
Israel radio said Defence Minister Binyamin Ben-Eliezer told a cabinet meeting on Sunday that the attacks were in retaliation for a recent increase in mortar attacks.
Palestinian witnesses denied mortar shells were made at the factory. They said the real products were machines for cutting wood and marble.
There were no reports of casualties.
Summit off
Israeli Prime Minister Ariel Sharon has cancelled a planned summit meeting with President George Bush in the United States next week.
An announcement from Mr Sharon's office said the trip - which was also to include talks in the UK - had been postponed indefinitely because of the security situation in Israel.
Our correspondent says there is speculation Mr Sharon may have wanted to avoid being pressured to withdraw Israeli troops from Palestinian areas.
The United States has been pushing Israel to resume talks with the Palestinians and pull out of the towns it occupied in the West Bank following the October assassination of Israeli tourism minister Rehavam Zeevi.
Washington is worried that Israel's actions will complicate its efforts to maintain support in the region for its campaign against Afghanistan's ruling Taleban.
Israeli Prime Minister Ariel Sharon has said his forces would only withdraw when the Palestinian Authority had outlawed militant groups and handed over those responsible for Mr Zeevi's assassination.
Arab League Secretary-General Amr Mussa added to calls for progress on a Middle East settlement on Sunday.
Speaking ahead of a meeting with 10 Arab foreign ministers, he said a new peace deal between Israel and the Palestinians must have as one of its aims the establishment of a Palestinian state.