The sightings occurred within minutes of each other on Saturday near the US-Mexico border.

ABC News obtained an audio clip of a conversation between the two pilots and the Albuquerque Air Route Traffic Control Centre.

While around 37,000 feet above the ground, a pilot flying a small aircraft manufactured by Canadian firm Learjet asks the controller: “Was anybody above us that passed us like 30 seconds ago?”

He responds: “Negative.”

“OK, something did,” says the pilot of the Learjet plane.

Another pilot then says: “It’s a UFO.”

Minutes later, the controller contacts an American Airlines pilot flying an Airbus aircraft to look out for anything “passing over” in the next 15 miles.

The Learjet pilot joins in, saying: ”I don’t know what it was, it wasn’t an aeroplane … the path was going in the opposite direction.”

Seconds later, the Airbus pilot says: “Yeah, something just passed over us … I don’t know what it was. But it was at least two, three thousand feet above us. Yeah, it passed right over the top of us.”

The controller later asks: “American 1095, can you tell if it was in motion or just hovering?”

The pilot says: “Couldn’t make it out whether it was a balloon or whatnot. But it was just really beaming light or could have had a big reflection and was several thousand feet above us going opposite direction.”

It comes after it emerged the Pentagon ran a secret programme investigating UFO sightings between 2007 and 2012.

Although the Advanced Aviation Threat Identification Programme officially ended five years ago, when US defence officials shifted attention and funding to other priorities, it remains unclear if the US continues to investigate sightings of mysterious flying objects.

The programme was given $22m (£15m) in annual funding, which was hidden in US Defence Department budgets, The New York Times reported.

Source: Independent