The militant groups Hamas and Islamic Jihad both claimed responsibility. Palestinian Prime Minister Mahmoud Abbas condemned the bombing as a "terrible act."
The bombing threatened to derail the U.S.-backed "road map" peace plan. In a first move, Israel called off the planned handover of the West Bank towns of Jericho and Qalqiliya to Palestinian control. The handover was to have taken place later this week.
The blast went off shortly after 9 p.m. Tuesday, as the crowded tandem bus — which has two passenger sections — drove along a main thoroughfare in Jerusalem and another bus pulled in front of it, witnesses said.
The attack followed a deadly explosion set off by a suicide bomber outside the hotel housing the U.N. headquarters in Baghdad. A government spokesman said there was no known direct link between the two bombings, although he said the motivations were similar.
"It is motivated by extremist Islamist militants who don't accept the legitimacy of the West or of Israel," government spokesman Dore Gold said.
"It was the No. 2 bus that came from the Western Wall," said a motorist, Jacob Bitnovsky. "I heard a huge blast and when I turned around I saw parts of the bus flying everywhere. I got out of the car and ran. There was a lot of smoke and running, saw a child on the ground gasping for air."
Several children were among the wounded in Jerusalem.
"About half of the 41 injured who came to our hospital were children," Professor Yonatan Levy, director of the Shaarei Tzedek hospital, told reporters.
Strollers were scattered near the stricken bus, medics carried away several crying children with tattered clothes and blood-smeared faces, and a baby girl died in a hospital before doctors could find her parents.
"It is important for people to understand that the children who died and were injured were specifically targeted by the suicide bomber who saw them," Gold said.
The bus had started out at the Western Wall, Judaism's holiest shrine, and was headed to an ultra-Orthodox Jewish neighborhood.
One report said among the passengers were members of a family who had celebrated a Bar Mitzvah, the Jewish rite of passage into adulthood for boys, at the Western Wall.
A second bus passing nearby when the explosion went off was also badly damaged, with windows blown out. Rescuers had to use blow torches to get out some of the wounded.
"What is clear is that it was a very big bomb," said Jerusalem fire chief Amnon Amir.
CBS News Correspondent Tom Fenton reports the explosion echoed through the neighborhood, with the debris, bodies and body parts littering the pavement.
Paramedics treated wounded on the sidewalk, and body parts were strewn about.
Police spokesman Gil Kleiman, Israel Army Radio and rescue service workers first put the number of dead at 20, then lowered the number to 18. Israeli officials don't include the bomber in the death toll. Fourteen of the wounded were in critical condition.
In Washington, the White House deplored the bombing and offered sympathies to the victims and their families.
"We condemn this vicious act of terrorism," said Sean McCormack, a spokesman on national security issues. "We call on the Palestinian Authority to dismantle terrorism."
CBS News Correspondent Mark Knoller, reports the U.S. is once again calling on the Palestinian Authority to take action to dismantle terrorist groups. But the White House is not giving up on the peace process — saying the U.S. commitment to it remains strong.
Gold, the Israeli government spokesman, said Israel was paying the price for the Palestinian Authority's inability to rein in militants.
"Israel will have to protect it's population," he said, saying Israeli leaders had yet to decide on their response.
The explosion went off as Abbas was meeting with Islamic Jihad in the Gaza Strip to persuade them to halt attacks on Israelis. Abbas said he has asked Palestinian security forces to investigate.
Palestinian militants declared a unilateral truce on June 29, but have said they would continue taking revenge for Israeli killings of their operatives.
Last week, Islamic Jihad threatened attacks on Israelis to avenge the killing of a senior operative, Mohammed Sidr, in an Israeli arrest raid in the West Bank city of Hebron.
In a phone call to journalists, Islamic Jihad claimed responsibility for Tuesday's bombing, saying it was in revenge for the killing of Sidr, whom Israel has accused of plotting a series of attacks.
Later Tuesday, Hamas distributed fliers in Hebron, saying the Jerusalem bombing was carried out by one of its supporters, identified as Raed Abdel-Hamed Mesk, 29.
In the Gaza Strip, a Hamas leader, Abdel Aziz Rantisi, insisted Hamas was not involved. "We are committed to the truce. I don't know who carried out this action," Rantisi said.