Video footage has emerged of the moment one of the US president's official planes flew just above Manhattan's financial district, sparking fears among New Yorkers of a September 11-style attack.

The Boeing 747, which becomes Air Force One when used by the president, and an F-16 jet circled the Statue of Liberty and the lower Manhattan skyline near the World Trade Centre site yesterday morning. Workers evacuated offices and emergency services were inundated with calls.

In the footage filmed from the Barclays Capital building the plane can be seen apparently flying close to buildings.

The individual who took the video told the Guardian: "There was so much panic and people in my building had to go home and one pregnant woman had to go to hospital."

He said the woman was OK but he couldn't believe the official explanation for the flyover, which was that it was a photo opportunity, one of a series of flights to get pictures of the president's airliner in front of national landmarks.

Even the New York mayor, Michael Bloomberg, did not know about it, and said it was "insensitive" to fly so near the site of the 2001 attacks.

"Why the defence department wanted to do a photo op right around the site of the World Trade Centre catastrophe defies the imagination," he said. "Poor judgment would be a nice ways to phrase it ... Had I known about it, I would have called them right away and asked them not to."

There was also criticism, coupled with scepticism about the official explanation, on the blogosphere. On the abovetopsecret forum, Highground wrote: "Perhaps 'they' are gauging what a certain area will do in the event of such an attack in the future." On the same site, Riley suggested Air Force One "had to make a detour because of a security threat".

The director of the White House military office, Louis Caldera, took the blame a few hours later.

"Last week, I approved a mission over New York. I take responsibility for that decision," Caldera said. "While federal authorities took the proper steps to notify state and local authorities in New York and New Jersey, it's clear that the mission created confusion and disruption. I apologise and take responsibility for any distress that flight caused."

Federal officials provided few other details and would not say why the public and area building security managers weren't notified.

President Barack Obama was furious, a White House official who did not wish to be identified told the Associated Press.

An Air Force combat photographer took pictures from one of the fighter jets, administration officials said.

The photo opportunity was combined with a training exercise to save money, according to another administration official.

The Federal Aviation Authority (FAA) notified the New York police department (NYPD) of the flyover, telling them photos of the Air Force One jet would be taken about 1,500ft (450 metres) above the Statue of Liberty on Monday morning. It had a classified footnote that said "information in this document shall not be released to the public or the media".

NYPD spokesman Paul Browne said typically a flight like this would be publicised to avoid causing a panic, but they were under orders not to in this case.

The FAA also alerted an official in the mayor's office, but he didn't tell Bloomberg, who said he first learned about it when his "BlackBerry (mobile phone) went off crazy with people complaining about it".