The FBI (search) on Tuesday warned local law enforcement officials to be on the alert for a possible terror attack within the United States.
The bulletin was described as a continuation of the one issued late Friday, which warned Americans of possible terror attacks abroad.
Homeland Security Secretary Tom Ridge (search) was going to the White House Tuesday afternoon to meet with President Bush and the Homeland Security Council to discuss "threat and intelligence information."
A Department of Homeland Security spokesman would not comment on whether those discussions would include raising the national threat level.
White House spokesman Ari Fleischer said Tuesday that the national alert status remained unchanged at yellow, an "elevated" level in the mid-range of the five-tier warning scale. A DHS spokeswoman said there were no plans to raise the level to orange, or "high."
One law enforcement official told Fox News that Tuesday's FBI message went out because the intelligence community is hearing "chatter" that indicates there is a concern of an Al Qaeda (search) attack within the U.S.
Last week's terror attacks in Saudi Arabia and Morocco, believed to have the fingerprints of Al Qaeda all over them, show that the terror network is desperate -- diminished but not yet destroyed, the official said.
"We could see more attacks from Al Qaeda either in Europe or inside the U.S. in coming days," a U.S. official told Fox News.
The official told Fox that although a lot of "chatter" on possible threats comes through on a regular basis, "quantity can be misleading when it comes to these threats. This stuff is quality. There is more concern about this information that we're getting because it is coming from quality sources ... a number of them.
"There is a legitimate cause for concern."
The source said the information is more solid than that which led to raising the terror level in the past.
Fleischer acknowledged the increase in "chatter" and said, "we've seen this before." He added that the Bush administration wants to remain "vigilant."
Last week's terror attacks in Saudi Arabia and Morocco "may be a prelude to an attack on the U.S.," the FBI said in its bulletin on Tuesday. But the agency said it has no specific information indicating a target or a planned attack.
The FBI is helping Saudi authorities investigate last week's homicide bombings on three Riyadh housing compounds in which 25 people, including eight Americans, were killed. Al Qaeda is thought to be responsible for that bombing, as well as the bomb attacks Friday in Casablanca that killed 41 people.
In the warning issued Friday, the FBI said Usama bin Laden's Al Qaeda terror network "likely" may be planning attacks against American and Western targets and "attacks in the U.S. cannot be ruled out."
It said the homicide car bombings in the Saudi capital indicate "further refinement in Al Qaeda operational capabilities.''
"The May 12 bombings in Saudi Arabia indicate that the Al Qaeda network remains active and highly capable," the FBI said. "The U.S. intelligence community assesses that attacks against U.S. and Western targets overseas are likely; attacks in the United States cannot be ruled out.''
U.S. counterterrorism officials have said the bulk of the intelligence points to possible strikes overseas.
Saudi Arabia's ambassador to Washington, Prince Bandar bin Sultan, told reporters in Riyadh that "there is chatter, a high level of chatter regionally and in other international spots" about possible new attacks in Saudi Arabia or America.
"I think the news that many Americans woke up with this morning, that we made the decision to close our embassy and several consulates in Saudi Arabia, is jarring, but also it's a grim reminder of events in Saudi Arabia and perhaps Morocco as well, proof that this war on terrorism is far from over," Rep. Mike Pence, R-Ind., told Fox News Tuesday. "The American people need to be vigilant."
"Al Qaeda has demonstrated an ability to reorganize, to restructure … they continue to plan against us and we'll continue to fight against them," said Rep. Steve Israel, D-N.Y.
The FBI on Friday said in its bulletin that "state and local law enforcement agencies" should remain vigilant to potential indicators of pre-operational planning, such as target surveillance and acquisition of explosives material.
"The Al Qaeda network and other international terrorist groups have demonstrated the ability to plan and carry out complex, simultaneous attacks against multiple targets."
Friday's bulletin described the Riyadh bombings in detail and listed similarities between the attacks on the compounds:
• The use of two vehicles, including a sedan-type passenger automobile followed by a larger sport-utility-type vehicle or small truck capable of carrying a VBIED (vehicle-borne improvised explosive device), as well as additional armed operatives.
• The use of "dismounted'' gunmen to engage guards and penetrate security countermeasures.
• Pre-operational planning and surveillance
• Targeting of "soft'' or lightly-secured sites
• A focus on causing mass casualties
"Further, these attacks suggest that Al Qaeda may be deterred by enhanced security and changes in the security countermeasures adopted by potential targets," the FBI said. "Al Qaeda operatives will adapt their targeting to maximize the likelihood of operational success, selecting softer targets if more hardened sites are considered too difficult to attack successfully.''
The FBI has previously warned that terrorists could strike apartment buildings, hotels, restaurants and businesses.
Fox News' Bret Baier, Catherine Loper, Ian McCaleb and Anna Stolley and the Associated Press contributed to this report.