The top Democrat on the Senate Intelligence Committee said Sunday that a major terrorist attack on the United States is "in the realm of possibility" following violence in Paris this week, though there is no credible information about a specific plot.

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Sen. Dianne FeinsteinDianne Emiel FeinsteinFeinstein's office says it has received threats over Kavanaugh Dem senator praises Ford opening the door to testifying The chaos in the Kavanaugh nomination illustrates the high stakes of the Supreme Court MORE (D-Calif.) also said that sleeper terrorist cells exist in the United States as well as France, suggesting that surprise attacks are not just a threat for Europe.

"This calls for vigilance," Feinstein said on CNN's "State of the Union."

"It calls for making sure the national security agencies of our countries [are prepared]. The French are good at it; so are the British and the Germans. Hopefully we can be even more active in doing things that will help us to find terrorists, see how they're communicating and to track that."

Still, Feinstein acknowledged that tracking international terrorists as they move from country to country is "extraordinarily difficult."

"[The French] had these people under surveillance for a substantial period of time," she said. "I don't know whether they've had cutbacks or what, but this has to now be all-out … The way you stop this is intelligence."

The comments came as France braces for the possibility of more violence as world leaders march in the streets of Paris to mark last week's 17 deaths.

Feinstein said countries need to "deal with" terrorist propaganda materials and bomb-making directions that circulate freely online.

"When you have a recipe for a very serious bomb out there on the Internet, we need to deal with it," she said. "We know the people who put it there intend to have it used for a terror attack."