The 9/11 attacks are not a matter of history because Islamic extremists are still at war with the United States, said Rudy Giuliani, New York's mayor at the time of the terrorist attacks 13 years ago Thursday.
Remembrance ceremonies were being held throughout the day in New York, at the Pentagon, and in Shanksville, Pennsylvania.
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"We can never not be vigilant," Giuliani said in a CNBC interview. He added that Americans are safer today due to the "tremendous" homeland security efforts of the George W. Bush and Barack Obama administrations.
Giuliani, dubbed "America's Mayor" for his high-profile efforts in the wake of the attacks, said on "Squawk Box" that people who said New York City would never recover from the attacks were proved wrong.
"Resiliency can be defense against terrorism," he said.
—By CNBC's Matthew J. Belvedere