Security has been increased across the United States, with the country's alert status raised to orange - the second-highest level - following renewed threats of attacks.
America will be honouring its war dead this weekend
With Americans preparing for the Memorial Day long weekend, the authorities are urging citizens to be extra vigilant but not to change their plans.
Security has been boosted at what are considered to be high-profile targets in the major cities.
The alert was issued as the US, Britain, Germany and Italy announced the temporary closure to the public of their embassies and consulates in Saudi Arabia amid fears of "imminent" new terrorist attacks.
I'm confident we'll get them in the end. But the question is, will it be early enough or not?
Prince Bandar bin Sultan
Saudi ambassador to Washington
Saudi Arabia's ambassador to Washington, Prince Bandar bin Sultan, said electronic "chatter" indicated a follow-up was being planned to the suicide attacks which took place last week in Riyadh.
Saudi authorities say they are questioning three suspected members of al-Qaeda who were arrested in Jeddah on Monday.
'Warnings to Muslims'
National Guardsmen have been deployed to protect New York's subway system and security has also been boosted at the Sears Tower in Chicago and the Golden Gate Bridge in San Francisco.
"The US intelligence community believes that al-Qaeda has entered an operational period worldwide, and this may include attacks in the United States," US Homeland Security Secretary Tom Ridge said.
Possible terror tactics, he said, included "small-arm-equipped assault teams, large vehicle-borne explosive devices and suicide bombers".
ABC news has been quoting two e-mails intercepted by US intelligence which it said it had obtained from an FBI bulletin.
One warns of a "possible devastating attack in the next 48 hours" and urges all Muslims to leave all cities, especially Boston and New York.
The other mentions Washington DC and New York as places for Muslims to avoid, as well as America's beaches.
The BBC's Justin Webb says the last time the US was put on the orange state of alert was during the war in Iraq.
The authorities now believe al-Qaeda may target the US to demonstrate it is still viable, he adds.
Mr Ridge has also encouraged state governors and city mayors to deploy extra police across the nation.
Our correspondent says that most will comply, but the costs are high, and complaints are growing that without specific intelligence, the alert system causes alarm without doing much practical good.
The US consulate in Dhahran as well as the UK trade office in al-Khobar are also being closed to the public.
The BBC's Zubeida Malik, in Riyadh, says the Saudis believe there are about 50 hardcore militants in the country, with hundreds of sympathisers.
Ordinary life goes on, our correspondent adds, but Saudis are preparing for the worst - worried about stability at home, and the perception of their country abroad.
The US may not reopen its offices before Sunday, a message on the US Embassy's website said.
The UK Foreign Secretary, Jack Straw, said the closure of British missions would last for at least the next few days.
A German foreign ministry spokesman said the German embassy in Riyadh and a mission in Jeddah would remain closed at least until Friday. The Italian embassy was also closing its doors to the public on Wednesday.
Al-Qaeda has been blamed for the Saudi attacks
US State Department spokesman Richard Boucher said it was prudent to take "precautionary" measures as al-Qaeda remained a threat in Saudi Arabia.
Saudi Prince Bandar told journalists he was confident of catching the terrorists but wondered if it would be "early enough or not".
The suicide attacks on Riyadh, which left 34 people dead, came two weeks after the US announced it was withdrawing most of its troops from Saudi Arabia, where they were deployed during the 1991 Gulf War.
BBC security correspondent Frank Gardner says three al-Qaeda cells were believed to have been active in Saudi Arabia prior to last week's attacks.
One is reported to have been destroyed, one to have fled abroad and the third to remain active inside the country.
But the threat, he said, was not specific to Saudi Arabia - Egypt, Jordan, Yemen and Pakistan were also likely targets.