The FBI also warned that US interests overseas may be at risk.
The caution came as the American Senate passed a bill giving police extra powers to counter terrorism. It gives them broader authority to tap telephones, and the right to detain immigrants suspected of terrorism for up to seven days.
The House of Representatives is expected to approve similar legislation later on Friday.
US Attorney General John Ashcroft warned last month that there could be fresh attacks on America once it retaliated following the 11 September atrocities.
That retaliation continued into the night on Thursday, as American warplanes launched a series of raids on the Afghan capital, Kabul.
'Credible' threat
The FBI said it had received information which leads it to believe that the threats of more terrorist activity were credible.
It says it has asked all local law enforcement agencies to be on the highest alert, and has called on people to be vigilant.
President George W Bush, in a press conference on Thursday evening, said it was a general rather than specific threat, and that it may not be the last.
In other developments:
The Senate legislation is aimed at increasing the police's ability to intercept such attacks.
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It is also calling for 11 September to be declared a day of remembrance which would be marked annually with a minute's silence and the flying of flags at half-mast.
'Huge fireball'
The US entered its fifth night of attacks on Afghanistan on Thursday night to "smoke out" Bin Laden.
Several loud explosions could be heard in the east of Kabul near a Taleban military base, and a huge fireball lit the sky to the south of the city with a munitions dump reported hit.
There were also reports of explosions around the Taleban stronghold of Kandahar, to the south
The US has denied Taleban claims that it has targeted civilians. The Taleban say more than 140 people had been killed in the last 24 hours.
The US Defence Secretary, Donald Rumsfeld, said unintended loss of life was inevitable in any military engagement but said the United States did not target civilians.
He also said the Taleban were still in a position, as he put it, to threaten US aircraft. He pointed out they still had anti-aircraft batteries, stinger and surface-to-air missiles as well as helicopters and planes.
Pakistani soldiers are deployed in Quetta and other cities to prevent outbreaks of violence ahead of pro-Taleban rallies due on Friday
The FBI's warning of further terrorist attacks in the US came during a week of several nerve-wracking incidents in the country.
The FBI has launched a criminal investigation in Florida after a third case of anthrax was detected on Thursday. A 63-year-old photo editor died from the disease earlier this month.
And two domestic flights had to be curtailed following passenger disturbances.