Updated

Terrorism intelligence in Saudi Arabia (search) suggests a major attack could take place in the next six weeks, a defense official said, but there are no specifics on the target.

The State Department (search) recommended Wednesday that diplomats' families should leave Saudi Arabia. A U.S. counterterrorism official, who spoke on condition of anonymity, said no single specific threat or piece of intelligence triggered the department's recommendation.

Instead, the decision was based on a review of the entire terrorism situation in the kingdom, the official said.

"We've seen an increased threat level to Western and American interests in Saudi Arabia, particularly," Deputy Secretary of State Richard Armitage said Thursday.

Al Qaeda (search) probably does not have the wherewithal to launch a sustained offensive inside Saudi Arabia right now, but enough operatives remain to pull off homicide bombings such as the ones that have hit the country in recent months, a U.S. counterterrorism official said, speaking on the condition of anonymity.

In the Saudi capital of Riyadh, meanwhile, security was tight Thursday, with a heavy police presence throughout much of the city. Armored personnel carriers and heavily armed soldiers were stationed outside of Western housing compounds and at key intersections, and police and soldiers manned roadblocks and checkpoints.

There was also beefed up security outside the diplomatic quarter, where a number of Western embassies are located.

Al Qaeda's operation in Saudi Arabia has suffered repeated blows since May, when the kingdom's security services launched a crackdown against militants. Some leaders were captured and killed, and cells in Mecca and elsewhere were disrupted.

The Saudis have been "going after these terrorists and trying to tear them out root and branch," Armitage told CBS' "The Early Show." "The problem is there are many cells and it takes a while to dig them out."

Because of the crackdown, Al Qaeda probably can't begin any type of major offensive, the counterterrorism official said, but is still capable of launching homicide bombings like a Nov. 8 strike at the Muhaya housing compound in Riyadh that killed 17.

In its warning on Wednesday, the State Department recommended that nonessential American diplomats and the families of all U.S. officials in Saudi Arabia depart.

The department also recommended that private U.S. citizens consider leaving as well. Americans making plans to go to Saudi Arabia were advised to defer any such travel in light of "the potential for further terrorist activities."

"We remain fully confident that Saudi authorities are doing everything they can to protect their citizens and foreign nationals in the kingdom against terrorist attacks," department spokesman Lou Fintor said. He said the department's decision was "based on the reality that the terrorist threat in Saudi Arabia remains at a critical level."

The departure of U.S. officials and family members was not ordered, but was voluntary. Expenses were to be paid by the U.S. government.

The indications of terrorist threats include the targeting of transportation, the department said.

"American citizens in Saudi Arabia should remain vigilant, particularly in public places associated with the Western community," the department said.

There are some 200 to 300 nonessential U.S. officials and family members in Saudi Arabia, and some 30,000 U.S. citizens in all.

U.S. officials say the top Al Qaeda figure in Saudi Arabia is Abdulaziz Issa Abdul-Mohsin al-Moqrin, also known as Abu Hazim. He took over when Yousif Salih Fahad Al-Ayeeri -- "Swift Sword" -- was killed in a shootout late in May.

The violence in Saudi started in May with homicide bombings at three housing projects in May. Thirty-five people, including nine attackers were killed.

The State Department responded then by ordering nonessential U.S. officials and family members to depart.

Weeks later, Al-Ayeeri was killed and another senior operative, Abu Bakr al-Azdi, turned himself in. In both June and November, Saudi security forces raided cells in Mecca and disrupted bomb-making operations.

Police arrested a Saudi citizen believed to have helped smuggle the weapons used in the attack, the Saudi daily Okaz reported Wednesday.

Saudi officials say most of the weapons used in militant operations in Saudi Arabia -- including the May homicide attacks -- were smuggled from Yemen.

The diplomatic quarter east of Riyadh has been guarded heavily by Saudi armed forces since the suicide attacks. Travel by American officials and their families in Riyadh is restricted already to the hours between 6 a.m. and 6 p.m.

Americans who travel to Saudi Arabia or remain there despite the warning were told to register with the U.S. Embassy in Riyadh or the consulates in Jeddah and Dhahran so arrangements can be made to keep them up to date.