Officials say attacks could match 11 September
US security sources have indicated that al-Qaeda may be planning new attacks, and that these might involve planting bombs in apartment buildings.
Mr Cheney also defended the Bush administration's handling of reports on al-Qaeda activity prior to the September attacks, while acknowledging that intelligence agencies had failed to pool their information.
"We don't know if it's going to be tomorrow or next week or next year," said the vice president, adding that the US had had "some success" in disrupting al-Qaeda's network.
The militants, led by Osama Bin Laden, are believed to have organised the suicide attacks on 11 September, which killed about 3,000 people in New York, Washington, and Pennsylvania.
US National Security Advisor Condoleezza Rice said on Sunday that the US was on a far higher state of terror alert now than it was before those attacks.
'Chatter in the system'
Intelligence specialists have said there has been an increase in the volume of messages between al-Qaeda cells, similar to that noted before 11 September.
An FBI spokeswoman, Debbie Weierman, said members of the network had reportedly been "considering renting apartments in unspecified areas of the United States and then planting explosives".
A senior Bush administration official quoted by the New York Times suggested that the new intelligence reports had yet to form a coherent picture.
"There's just a lot of chatter in the system again," the official said.
But a recent suicide bombing in Karachi, Pakistan, and an attack on a synagogue in Tunisia are seen as evidence by US intelligence officials that al-Qaeda still has the potential to stage deadly attacks.
Bush under fire
The Bush administration has defended its failure to foresee the 11 September attacks, saying the information was too vague to indicate the hijackers' precise plan.
"I still have a deep sense of anger that anyone would suggest that the president of the United States had advance knowledge that he failed to act on," said Mr Cheney on Sunday.
But he accepted that there had been a failure on the part of the intelligence agencies to coordinate their anti-terrorist activities - an institutional failure, he argued, which was not the fault of President Bush.
In recent days, it has emerged that several memos and reports had been passed on to officials which pointed to a planned attack.
President Bush spoke out on Friday, saying he would have done everything in his power to stop the attacks if he had known in advance.
But critics have demanded an inquiry into the intelligence failure and senior Democrats accuse the Republican administration of trying to stifle legitimate debate.