It's unclear what the object is, and the pilots are heard laughing and shouting as they attempt to track it.
As they continue to follow the object traveling at a high rate of speed, one pilot is in awe, saying, "Oh my gosh, dude". "Look at that flying!" he says.
Mellon, who is also an advisor to the private research firm called To the Stars Academy of Arts and Science, wrote that the sightings of highly advanced aircrafts much superior to the ones in the United States have hinted at a possibility of some countries going much ahead of others in technology or an evidence of an alien civilization.
The organization notes that the object has no wings or tail, and leaves no exhaust plume. It was started by Tom DeLonge, the former singer and guitarist for the rock band Blink-182.
The location and other key information about the video was not announced.
In a Washington Post op-ed, Mellon, who now works at The Stars Academy of Arts and Science (TTSA), says some USA pilots have encountered a UFO and several have even caught footage of the occurrence, but not enough has been done about it.
"These are just three videos now that have come out that everybody's looking at", Elizondo told CNN Monday. "But there is far more compelling evidence that I was privy to that - you know, I think you're looking at the tip of the iceberg".
Countries like China, Russia, and other European nations are willing to pursue this idea more than their American counterparts, according to Bigelow.
Chris Mellon, TTSA adviser and former deputy assistant secretary of defense for intelligence under presidents Clinton and George W. Bush, criticized the national security agencies for not researching what is behind the odd objects in the sky, ABC News reported.
On Monday, Elizondo also noted "eerie similarities" between the new video and the ones released a year ago, including the location in US airspace, the presence of US Navy pilots, the "Tic Tac" shape of the object and other signatures he said the videos shared in common.
He serves as an adviser to To The Stars Academy Of Arts And Science.
Mellon observed that military departments and agencies have instead treated "such incidents as isolated events rather than as part of a pattern requiring serious attention and investigation".
Speaking to the New York Times about the AATI programme, Bigelow said, "Internationally, we are the most backward country in the world on this issue".