The White House has been forced to apologise after one of President Barack Obama's official planes flew low over the Statue of Liberty, causing panic among New Yorkers.

Presidential 747 flies low over New York harbour

The low-flying plane unsettled New Yorkers. Photo courtesy of theage.com.au

Officials said the Boeing 747 - one of the aircraft designated as Air Force One when the President is on board - and an F-16 fighter jet escort were taking part in a photo opportunity.

But office workers panicked and fled their buildings as the image of two planes near the World Trade Centre site brought back memories of the September 11 terror attacks.

Mr Obama was not on board the 747 at the time and was reportedly "furious" about the incident.

New York Mayor Michael Bloomberg criticised the federal government and his own administration for failing to warn the public.

"The good news is it was nothing more than an inconsiderate, badly conceived and insensitive photo op with the taxpayers' money," he said.

President Barack Obama and first lady Michelle Obama waves as they disembark Air Force One at London's Stansted International Airport

Obamas on Air Force One in March

"They should know how sensitive people would be if they had low-flying planes down around the World Trade Centre site."

Mr Bloomberg blamed a breakdown in communications, saying he would have protested had he known in advance.

Louis Caldera, director of the White House Military Office, said he approved the mission and took responsibility for the decision.

"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, he said.

"I apologise and take responsibility for any distress that flight caused."

Employees at the New York Mercantile Exchange, Goldman Sachs and Merrill Lynch were among those who left their buildings, while hundreds of others called the 911 emergency line.