The FBI is warning state and local law enforcement agencies that al-Qaida could strike in the United States as well as at U.S. and Western interests overseas.
The FBI bulletin says the bombings in Riyadh, Saudi Arabia, show that al-Qaida is "active and highly capable."
It goes on to say that the U.S. intelligence community believes that such attacks overseas are likely, and that attacks in the U.S. cannot be ruled out.
The bulletin says the Saudi attacks featured "traditional hallmarks of al-Qaida operations."
Each bombing involved a sedan followed by a truck or sport utility vehicle full of explosives. Gunmen were used to attack guards and overcome security measures.
Thirty-four people were killed, including eight Americans.
Al-Qaida also is suspected in another series of bomb attacks Friday in Morocco that killed 41 people.
The FBI has warned before that apartment buildings, hotels, restaurants and businesses could be targeted.