More than 10 of the helicopters that carry tourists and executives around the Big Apple were gassed up with fuel containing metal particles that could have caused them to fall from the sky, The Post has learned.

A complaint about the potentially disastrous situation was filed with the Federal Aviation Administration by HeliNY, which runs sightseeing tours and charter flights out of the Downtown Manhattan Heliport at Pier 6 in the Financial District.

All helicopter operators in and around the city had “to ground their fleets while fuel lines in every machine could be tested,” HeliNY operations director Oyvind Vataker wrote in the complaint.

“Upon testing the fuel systems of all our aircraft, we found the same contamination in three of our six helicopters,” Vataker wrote. “This resulted in tremendous expense and opportunity cost due to the business we lost while the machines were down for maintenance to flush fuel lines and replace filters.”

The contaminated aviation gas was first discovered by an unidentified helicopter operator on Oct. 28, according to the complaint Vataker sent to the FAA, which is investigating.

Aviation expert Peter Field of Chesterfield, Mo., told The Post that metal particles in aviation gas can clog a helicopter’s fuel-injector nozzles and “could result in an engine failure.”

“Where can it come down and land, unless a heliport or the river?” Field said. “New York on both sides of the river is highly populated and there’s almost no place to come down.”

In his letter, Vataker said that Manhattan’s East 30th Street and West 34th Street heliports had apparently been ruled out as the source of the contamination.

All but one of the whirlybirds with dirty gas fueled up at Pier 6 and, according to the complaint, a prime suspect is allegedly Saker Aviation Services, which runs the heliport there, he said.

“Saker has a responsibility to test every shipment of fuel it receives prior to pumping, and to continuously test the lines in their fuel farm intermittently to make sure it is clear of contaminants,” Vataker wrote.

“If they failed to do so, this is negligence with a tremendous monetary cost to my company and others, and it could have had a potentially disastrous outcome.”

A FAA spokesperson confirmed that the agency was probing the source of the dirty gas but declined to comment further.

In a statement, Saker — a publicly traded company that also runs the Garden City Regional Airport in Kansas — said, “There is no indication that there was any contamination in our fuel system.”

“In the 15 years we have operated the heliport we have never had an issue of this nature,” the company said. “Saker works constantly with the FAA and will continue to provide any information requested of us.”

Saker director and spokesperson Sam Goldstein also said Monday that Vataker’s letter was mistaken and that the contaminated fuel was discovered on Nov. 4 by Zip Aviation, which also operates out of the Pier 6 heliport.

Goldstein said Saker’s fuel system at the heliport has been out of service since Oct. 28 due to an unspecified leak.

He also released a Nov. 4 “contaminated fuel alert” email sent by the Eastern Region Helicopter Council, an industry group, to its members.

“One of our operators has reported a contaminated fuel issue in multiple ships in their fleet. The operator reported buying fuel from every heliport and numerous airports in the area,” the email said.

It added: “We suggest that you check your fuel filters if you have bought fuel in the local NY/NJ area.”

Vataker said Monday that the letter he signed and sent to the FAA was written by a lawyer and that he could not explain why it said the tainted fuel was discovered on Oct. 28.

Zip Aviation didn’t immediately return a request for comment.

More than 30 people have died in Big Apple chopper mishaps since 1977, including five passengers who drowned in the East River when one of their harness tethers got tangled around the fuel shut-off lever, killing power to the rotors.

Those victims were on a “doors-off” sightseeing trip, which led the FAA to ban such flights unless the passengers wear government-approved restraints.