JFK Jr.’s body was found 116 feet below the Atlantic Ocean — just hours after the search team began discussing calling off the massive operation, the mission’s leader told The Post.

After John F. Kennedy Jr.’s plane went missing on the night of July 16, 1999, the US government embarked on one of the largest maritime searches for private citizens in the nation’s history.

On the fourth day of what had been an exhausting and fruitless effort to find Kennedy, his wife, Carolyn Bessette, and her sister, Lauren, officials began planning an exit strategy.

But as they discussed ending the search, high-tech sonar scanners, almost miraculously, finally located Kennedy’s body on the ocean floor, about 10 feet from the wreckage which still held the strapped-in bodies of the sisters.

They were about seven miles off the southwest coast of Martha’s Vineyard.

“John F. Kennedy Jr. was outside the aircraft, and there was a consideration that had another day passed, that in the 1.6-knot current, that he might’ve been swept away,” said Coast Guard Capt. W. Russell “Russ” Webster, the incident commander for search operations for the JFK Jr. mission.

“They might have never found him had another day gone by,” his wife, maritime historian Theresa Mitchell Webster, recalled.

The couple co-authored “The Last Flight: The Untold Story of the Search for JFK Jr. and the Race Against the Atlantic,” which describes how side-scanning sonar and a video camera located America’s Son.

The following morning, five days after the crash of the Saratoga II that Kennedy, 38, was piloting in dense haze, divers recovered all three bodies.

Carolyn, 33, and Lauren, 34, were identified only through their different hair colors.

“The NTSB forensic anthropologist told us that the girls were not facially recognizable,” said Theresa.

The trio was traveling from Caldwell, NJ, en route to Martha’s Vineyard, for Kennedy’s cousin Rory’s wedding.

Kennedy had been on visual flight rules, Russell explained, meaning, “the FAA was not tracking his plane, he was confident that he could navigate by site and geographic references, like lighthouses and factories,” since he had done the trip from New Jersey to Martha’s Vineyard 35 times before.

He relied on visual cues alone — since he had not yet completed his instrument training, having finished just 12 of 25 modules toward his certified flight instructor certification.

“On July 1st, 15 days before he flew, one of his certified flight instructors said, ‘John, you’re not ready yet for this. You need more experience with instruments,’” said Russell, who served in the Coast Guard for 26 years.

Kennedy’s inexperience with instruments hindered his ability to fly in poor visibility and could have caused spatial disorientation.

The National Transportation Safety Board report determined the plane fell at a rate of 4,700 feet per minute.

“Water is only marginally less than cement at that speed [almost 60 mph] and coming from that altitude,” Russell said.

The crew raced against the clock to find their bodies, the plane and their belongings, before human and animal scavengers did.

Russell, who worked on 10,000 missions in his career, estimates the operation — which spanned 100 nautical miles between Cape Cod and Long Island, and involved thousands of staffers from at least 28 local, state and federal agencies — cost up to $5 million.

The Websters took 15 years to research and write “The Last Flight,” which included close to 45 interviews.

“One of the reasons we were able to finally write this book was the fact that many of the people that had said they did not want to participate earlier had retired from federal service and became more talkative, more reflective. And they knew how important it was to tell this story,” Russell explained.

Theresa’s friend Maria Hooton — married to a close friend of Kennedy’s uncle, Sen. Ted Kennedy — was at the senator’s house the day after the plane went missing.

“She told us she saw John’s suit hanging in the laundry room that was pressed and ready to go,” she said.

During the mission, the Coast Guard received a number of “outlandish” calls, some from people who believed they were still alive.

“One was that John F. Kennedy Jr. was in an AOL chat room. People, I think, were grasping at straws,” Russell said.

The USCG also got a fax from an unnamed New York City spiritual organization that declared them deceased based on their analysis of their “magnetic auras.”

“The reason I remembered that so vividly was it was the very first external communication that we received on Sunday when the Unified Command Post opened up. And it was like, ‘Oh my God, this is so, so bizarre.’”