The warning comes ahead of the Asteroid Day to be observed on June 30. On that day in 1908, a small asteroid exploded over Tunguska in Russia's Siberia, levelling trees and burning the ground over 2,000 square kilometres.
This year, discussions and presentations will be streamed live from Luxembourg on June 30. Experts including Apollo 9 astronaut Rusty Schweickart and International Space Station astronaut Nicole Stott will answer questions from people on social media.
Mr Fitzsimmons said an unexpected strike today by an asteroid similar in size to the one that exploded over Siberia could easily destroy a major city, and a larger asteroid could be more dangerous.
"It is important to know that scientists and engineers have made great strides in detecting near-Earth asteroids and understanding the threat posed by them," Mr Fitzsimmons said.
"Astronomers find near-Earth asteroids every day and most are harmless. But it is still possible the next Tunguska would take us by surprise, and although we are much better at finding larger asteroids, that does us no good if we are not prepared to do something about them," he added.
The risk of a sizeable asteroid hitting the Earth is significantly growing every few years, Czech scientists who analysed 144 fireballs from a recent meteor shower had warned.
The Taurid meteor shower showed significantly enhanced activity in 2015. Researchers found that this was due to a well-defined orbital structure.
Researchers from the Astronomical Institute of the Czech Academy of Sciences recently showed that a "new branch" of Taurids contains at least two asteroids of the size 200-300 metres.