Bloomberg says the flyover so near the World Trade Center site showed "poor judgment" and was insensitive. He says he is furious that the NYPD and another city agency were notified last week, but did not tell him.
If he had known, Bloomberg says he would have tried to stop it.
The Federal Aviation Administration and the Air Force says the flight was a government photo opportunity and training mission involving a presidential plane.
Workers from several office buildings poured out onto the streets before they learned that the flights were innocuous.
John Leitner, a floor trader at the New York Mercantile Exchange Building, said about 1,000 people "went into a total panic" and ran out of the building around 10 a.m. after seeing the planes whiz by their building, near the World Trade Center site.
"Apparently, nobody in the building was informed that this was going to happen," he said. "Everyone panicked, as you can certainly understand."
He said the workers gathered along the Hudson River until a security officer with a bullhorn told them it was a planned exercise.
"The FAA and the presidential airlift group conducted an aerial photo mission" and training for crew members of the president's flying fleet, said Air Force spokeswoman Capt. Angela Webb. She declined to release any other information about the nature of the photos being taken.
She said the flight involved a VC-25, a Defense Department version of the 747 that is called Air Force One when the president is aboard, and an Air Force F-16 jet fighter. They flew over the upper New York Bay and Newark Bay between 10 a.m. and 10:30 a.m.
The Federal Aviation Administration said it notified city law enforcement about the mission.
The NYPD said the flight "was authorized by the FAA for the vicinity of the Statue of Liberty, with directives to local authorities not to disclose information about it, but to direct all inquiries to the FAA."
Among the workers who left their buildings were some at The Wall Street Journal.
Kathleen Seagriff, a staff assistant in the news rooms, said workers heard the roar of the planes and then saw them from their windows.
"They went down the Hudson, turned around and came back by the building," she said. "It was a scary scene, especially for those of us who were there on 9/11."
Some staffers, who thought they made out an American flag on one of the planes, stayed behind. But she said most didn't want to take the chance.
Webb did not know why the public wasn't notified ahead of time.
Sen. Charles Schumer blasted the FAA for the lack of warning.
"This was a photo shoot. There was no need for surprise," Schumer said. "There was no need to scare thousands of New Yorkers who still have the vivid memory of 9/11."
