One of the most significant targets, the tallest building in Los Angeles, known as the Library Tower.
A former CIA official says it was to be hit by a hijacked aircraft.
Robert Grenier, a former CIA counter-terrorism chief and now Managing Director of Kroll, Inc., "This was a serious serious plot. This was certainly well beyond the level of aspiration."
But intelligence sources say the CIA's ability to capture and break the 14 al Qaeda leaders stopped the plot against the Library Tower and more than a dozen others, including a hijacking at London's Heathrow airport, an attack on the U.S. consulate in Karachi Pakistan and a proposed anthrax attack.
"This program has been and remains one of the most vital tools in our war against the terrorists," President Bush said today.
The President described how the CIA produced a cascading series of arrests. Starting with the first of the captured al Qaeda leaders, Abu Zubaydah. Zubaydah had refused to cooperate until the CIA used what the President called an alternate set of interrogation procedures.
"Zubaydah was questioned using these procedures, and soon he began to provide information on key al Qaeda operatives," the President said.
That led the CIA to one of the plotters of the 9/ll attacks, Ramzi Bin al-Shibh, taken into custody in Pakistan.
He too was subjected to the CIA's procedures and quickly broke.
Giving up the location of his al Qaeda boss, Khalid Sheikh Mohammed, known as KSM, the mastermind of the 9/ll attacks.
"Once in our custody, KSM was questioned by the CIA using these procedures. And he soon provided information that helped us stop another planned attack on the United States," President Bush said.
The President would not reveal the CIA's interrogation procedures, but CIA officers have told ABC News they involve six escalating steps, ending in what's known as water boarding, in which prisoners are made to feel they are drowning.
Human rights groups call it torture, but the President disagreed.
"The United States does not torture," he said. "It's against our laws, and it's against our values. I have not authorized it, and I will not authorize it."
Hours before the President spoke today, the Pentagon released new rules of interrogation which outlawed water boarding.