One of Saddam's son-in-laws also said that Iraq hid its biological weapons programmes from UN inspectors, according to the tapes from August 1995, the television network reported on Wednesday.
The terrorist attack Saddam predicted could involve weapons of mass destruction.
"Terrorism is coming. I told the Americans," Saddam is heard saying, adding that he "told the British as well".
"In the future, what would prevent a booby-trapped car causing a nuclear explosion in Washington or a germ or a chemical one?" Saddam said. But he said Iraq would never carry out such an attack.
"This story is coming, but not from Iraq," he said.
The State Department had no comment on the report, which was broadcast on World News Tonight. ABC News said US officials confirmed that the tapes were authentic.
ABC News said the CIA found the tapes in Iraq and that the 12 hours were provided to it by Bill Tierney, a former member of a UN inspection team who was translating them for the FBI.
ABC News quoted Tierney as saying the US government was wrong to keep the tapes secret.
Tariq Aziz, the Iraqi deputy-prime minister, told Saddam on the tape that "the biological [attack] is very easy to make".
He said: "It is so simple that any biologist can make a bottle of germs and drop it into a water tower and kill 100,000. This is not done by a state. No need to accuse a state. An individual can do it."
Hussein Kamel, a son-in-law of Saddam's, who was then in charge of Iraq's weapons of mass destruction efforts, said that Iraq withheld information from the UN inspectors.
"We did not reveal all that we have," he said. "We did not reveal the volume of chemical weapons we had produced."
Hussein Kamel defected to Jordan shortly after the tapes were recorded, and Iraq admitted that it had concealed its biological weapons programme. Kamel returned to Iraq in February 1996 and was killed by security forces.
Charles Duelfer, who led the official US search for weapons of mass destruction after the first Gulf War, told ABC News the tapes show extensive deception but do not prove that weapons were still hidden in Iraq at the time of the US-led war in 2003.
"What they do is support the conclusion in the report which we made in the last couple of years, that the regime had the intention of building and rebuilding weapons of mass destruction, when circumstances permitted," he said.