The department official said the United States asked for increased security at all Western facilities in the country weeks before the suicide attacks at compounds in Riyadh.
The official, a Middle East expert who asked not to be identified by name, said the Saudi response fell short of the U.S. request.
Security issues continue to dog U.S.-Saudi relations. The State Department warned late Thursday of a possible terror attack in the Saudi city of Jiddah, a busy Red Sea port.
The warning said the city's U.S. consulate received unconfirmed information of a planned attack in the city's Al Hamra district. "Some consulate families resident in the district temporarily relocated to different quarters," said the alert, which was valid until June 15.
The earlier comment from the State Department official buttressed a statement on Wednesday by U.S. Ambassador Robert Jordan and appeared to contradict an account by Saudi Arabia's ambassador to the United States, Prince Bandar.
Bandar suggested that Jordan sought security for only one compound and that Saudi security successfully protected foreigners there.
"He asked for increased security at a certain compound," Bandar told CBS News. "We have passed it to the right authority, and that compound that he was concerned about was the only place that the evil people who did this attack did not cause injuries except killing the Saudi guards."
Appearing on ABC's "Good Morning America," Bandar said, "Our security agencies, ... the air force came to the conclusion there were adequate measures there."
The U.S. official said the request for Saudi cooperation was relayed by "VIP visitors" to Saudi Arabia last month, including the State Department's anti-terrorism chief, Cofer Black.
Another official said the Saudis asked for specificity about potential targets but the United States lacked such details.
The American sense of unease increased sharply two weeks ago. This was reflected in a public statement warning that terrorist groups might be in the final phases of planning attacks against U.S. interests in Saudi Arabia.
Stephen Hadley, deputy national security adviser for President Bush, visited Riyadh this past weekend to convey the administration's fears.
Hadley told the Saudis, according to a senior official, that there was a threat they needed to take seriously.
Attorney General John Ashcroft offered a somewhat upbeat view of Saudi cooperation.
"We believe we've had very good cooperation. ... We believe we want to upgrade our cooperation," he said at a news conference.
The adequacy of Saudi security measures should become clearer in the coming days with the arrival in the kingdom on Thursday of a six-member FBI team, which will work with Saudi officials.
More investigators and forensic experts will join the FBI team later. The Americans will seek Saudi cooperation in such key areas as interviewing witnesses and processing evidence.
That cooperation was slow in coming or nonexistent following the 1996 bombings of the Khobar Towers dormitory that killed 19 U.S. service personnel.
"They don't have a particularly good track record at cooperating," said retired FBI deputy director Weldon Kennedy. "They don't really follow through. They give lip service to cooperation."
The State Department official noted that not all steps taken by the Saudis to enhance security are necessarily relayed back to Washington.
The U.S. military has not increased security steps anywhere in the world this week because of new terrorist threats, a Pentagon official said Thursday, speaking on condition of anonymity.
The military distributes State Department travel warnings to troops who might be affected by them. Service members are given training on how to avoid terrorist attacks; they are not banned from visiting areas under terrorist threat.
Kenya is the latest potential terrorist attack site on the State Department's radar screen. A travel warning issued Wednesday night said terrorists may target civil aviation with shoulder-fired missiles.
"Terrorist actions may include suicide operations, bombings, or kidnappings," the statement said.