The chance of more Al Qaeda attacks against U.S. targets is  "almost a certainty," and Americans must stay vigilant, Vice President Dick Cheney said on Fox News Sunday.

"It could happen tomorrow, it could happen next week, it could happen next year, but they will keep trying. And we have to be prepared," Cheney said.

Asked if Usama bin Laden's network was planning to strike American targets, Cheney said: "We assume they are. There is certainly a level of noise out there in the system that would indicate that those efforts are continuing."

The "noise" Cheney was referring to was described as "increased Al Qaeda chatter" by anonymous U.S. officials in Saturday news reports.

The domestic reports followed a pan-Arab newspaper's report that an Al Qaeda leader was planning an attack against the U.S.

"There's a great temptation ... for people to look back at Sept. 11 and say, 'Well, we haven't been hit in eight months, therefore the threats have ceded or gone away.' I don't think that's the case at all," Cheney said.

The suggestion is that the network is reconstituting itself after a winter of disruptions caused by the U.S. military operations in Afghanistan and widespread arrests across the globe.

Cheney said the government is doing everything in its power "to make us a tougher target."

'Chatter' Overheard

Government sources told Fox News on Saturday that an increase in Al Qaeda activity had been detected and that there are indications that an attack of "equivalent magnitude" to the Sept. 11 attacks is a possibility.

Those officials said the information was overheard by government agencies listening to phone calls between members of Al Qaeda and obtained through interrogations and informants.

A similar increase in "chatter" occurred prior to Sept. 11.

The New York Times reported Saturday that the increased chatter was so general that the government could only take "broad defensive measures."

Earlier Saturday, the London-based Asharq al-Awsat newspaper quoted Abdel Azeem al-Muhajir, purportedly a "senior military leader" of Al Qaeda, as saying that the terrorist group's attack on a Tunisian synagogue last month will be followed by an upcoming attack on the United States. The Tunisian attack killed 19 people.

The U.S. attack would be "a more painful hit" than the Tunisian attack, according to the report.

An Associated Press source, however, described al-Muhajir as a midlevel administrator. In the interview with Asharq al-Awsat, al-Muhajir identified the truck driver who carried out the synagogue attack as Nizar Seif Eddin al-Tunisi, whose name had arisen before in the investigation of the attack.

Some officials speculated that the reports might only be bravado on the part of a crippled Al Qaeda. Sen. Charles Grassley, R-Iowa, said in an interview with Fox News' Rita Cosby that the reports should be taken seriously anyway.

"Considering what happened on Sept. 11, we ought to take all of these seriously, and we should not have a lull just because there's lots of warnings and we haven't actually been attacked," Grassley said.

Fox News' Carl Cameron, Rita Cosby and The Associated Press contributed to this report.