“The people who are worried about privacy have a legitimate worry,” Mr. Bloomberg said during a press conference in Midtown. “But we live in a complex word where you’re going to have to have a level of security greater than you did back in the olden days, if you will. And our laws and our interpretation of the Constitution, I think, have to change.”

Mr. Bloomberg, who has come under fire for the N.Y.P.D.’s monitoring of Muslim communities and other aggressive tactics, said the rest of the country needs to learn from the attacks.

“Look, we live in a very dangerous world. We know there are people who want to take away our freedoms. New Yorkers probably know that as much if not more than anybody else after the terrible tragedy of 9/11,” he said.

“We have to understand that in the world going forward, we’re going to have more cameras and that kind of stuff. That’s good in some sense, but it’s different from what we are used to,” he said.