In November 2004, U.S.-led forces launched an assault on the city to retake it from insurgents. Some of the fiercest fighting took place in southern Fallujah, where relatives said the bombers had lived.
Omar said family members of the bombers learned about their deaths through friends in Amman. He added that Rishawi and her husband left Fallujah a month ago.
In her televised appearance Sunday, Rishawi wore a black dress and white head scarf with tassels that dangled down her back. Her voice was even, devoid of emotion.
Rishawi said she and the three men were picked up in a white car and taken to Jordan. She said the driver of the car "was the one who arranged it."
"He had two explosive belts," she said, giving no further identification. "He made me wear one and he wore the other and taught me how to use it, how to pull and control it. He said we would carry it out in hotels in Jordan. We hired a car and went to the hotel."
Rishawi said that she and her husband entered a hotel, which Jordanian officials said was the Radisson. "He took a corner, and I took a corner," she explained. "There was a wedding in the hotel, children, women and men. My husband carried it out. I tried to carry it out, but it did not explode. I went out. The people started running and I ran away with them."
The terrorist attacks have rallied Jordanians. People have demonstrated peacefully in Amman to protest the violence, and another such gathering is planned for Monday. Motorists in the capital have attached Jordanian flags to the antennas and back windows of their cars.
In an interview with the Jordan News Agency, King Abdullah said the attacks were a turning point for his countrymen, who were now taking a stand against terrorism. "I know very well the courage of Jordanians, and their response to these events had exceeded all expectations," he said. "Jordanians are fearless, and terrorism will not affect their morale or their determination."
During a stop in Jerusalem on Sunday, Secretary of State Condoleezza Rice said the Amman bombings had served as a pivotal point across the Arab world. "In the aftermath of the vicious attacks in Jordan -- which killed dozens of people and wounded many more -- leaders and clerics and private citizens are now stepping forward and taking to the streets and calling this evil by its name," Rice said. "This is a profound change."
Rice said violence committed by Arabs against Arabs has led parents in the region to tell their children "to be engineers, not suicide bombers, to be voting citizens, not docile subjects."
The Rishawi confession dominated news in Amman on Sunday, and Jordanians were riveted by the sight of the plain-looking woman who had apparently set out to kill with abandon.
"No one can expect this strange attitude from such a woman," said Mejdi Nuaimat, 23, a computer engineering student. "It is very weird because we know that women do not have the same strength and belief in the issue of jihad like men. We do not consider this jihad; we consider it against Islam and against humanity."
Rafat Nasir, 30, manager of the De Cano cafe in Amman, said he was shocked by the disclosure that a woman might have been involved.
"In such a stable and secure country, no one can expect this terrified experience, especially in Amman," he said. "It is a new method of bringing a woman to explode herself in cold blood."
Staff writer Robin Wright in Jerusalem and special correspondents Naseer Mehdawi in Amman and Bassam Sebti in Baghdad contributed to this report.