Riyadh, Saudi Arabia ? The deadly car bombings of residential compounds in Riyadh could be followed by more attacks on Americans, U.S. officials warned Thursday.

A six-member FBI team came to the kingdom Thursday to determine what is needed to help in the investigation into Monday’s attacks, which killed 34 people, including eight Americans.

Thursday night the State Department issued a new warning to Americans in Jiddah, Saudi Arabia.

“The U.S. Consulate General in Jiddah has received an unconfirmed report that a possible terrorist attack in the Al Hamra district of Jeddah may occur in the near future. While we cannot certify the credibility of the threat, in light of recent events this information is being shared with the American Community. Some Consulate families resident in the Al Hamra district temporarily relocated to different quarters,” the warning said.

“U.S. citizens are encouraged to maintain a high level of vigilance and to take appropriate steps to increase their security awareness.”

As the investigation began, Robert Jordan, the U.S. ambassador to Saudi Arabia, said he expected “good cooperation” from the Saudis.

“I think both parties have learned from past experiences,” he told journalists at his residence. “There is a sincere, good-faith effort on both parts to cooperate, to work as partners to share information without jealousy or petty bureaucracy.”

The attack “was, if not the Saudi Sept. 11, it was certainly the Saudis’ Pearl Harbor,” Jordan added.

“This is a battleground rather than simply a nice place for civilians to live,” he said. “Everyone has to confront that.”

Saudi cooperation with the U.S. investigators could be critical. Some U.S. experts worry the Saudis will limit American access to suspects and evidence, as they did after the 1996 bombing of the Khobar Towers military dormitory that killed 19 U.S. service members.

Before the latest attacks, American intelligence uncovered evidence that groups were targeting Westerners and Americans, according to a U.S. official.