Mueller's prediction follows Vice President Dick Cheney’s recent warning that because no specific information is available, the United States is finding it difficult to respond to the latest intelligence hints that al-Qaida may be planning another attack.
Mueller said law enforcement has been somewhat successful in combating acts of terrorism in Northern Ireland by developing sources who could provide information about terrorist plans and by using electronic surveillance.
But he said the difficulty of getting informants inside terrorist groups targeting the United States makes it much harder to obtain advance information.
At the prosecutors meeting, Mueller said the FBI now believes that "an al-Qaida bomb maker" constructed the shoe bomb that Richard Reid had when he was apprehended aboard a flight from Paris to the United States in December.
Mueller made the comment in describing how the FBI is increasing its recruitment of scientific experts to help in terrorism investigations and is "centralizing analytical capability" to coordinate evidence gathering.