European police agency chief Rob Wainwright said the security landscape is "more difficult, more challenging" than at any time since the September 11, 2001 attacks.
It is an extremely dangerous time, stressed British Prime Minister David Cameroon, who said the threat was "severe" and an attack "is highly likely."
The three days of violence that left 17 dead in Paris last week -- starting when gunmen stormed into the offices of satirical newspaper Charlie Hebdo January 7 -- have left the world reeling, with questions being raised about how the perpetrators slipped through the cracks.
Cherif and a third gunman, Amedy Coulibaly, who killed four hostages at a Jewish supermarket, had each spent time in jail where they were further radicalized.
Also Read
The challenge has shifted since Al Qaeda's hey day under Osama Bin Laden, Wainwright stressed.
Police are seeing "a lot of independent or semi- independent people" who have been radicalized through the Internet or through experience fighting in Syria and Iraq, he told ABC's "This Week" in an interview that aired Sunday.
"It's much looser than we have seen before. It's not the same as in the days of 9/11, when we had an identifiable command and control structure."
US Senator Richard Burr said the Paris assault should trigger a re-evaluation of how authorities monitor possible threats.
"Every country in the world today is probably looking back at the policies that they've got on surveillance for known fighters," the Republican lawmaker said in an interview on CNN's "State of the Union."
But British leader Cameron stressed that dealing with the problem of extremists "is going to take a very long time."