WASHINGTON — The strange objects, one of them like a spinning top moving against the wind, appeared almost daily from the summer of 2014 to March 2015, high in the skies over the East Coast. Navy pilots reported to their superiors that the objects had no visible engine or infrared exhaust plumes, but that they could reach 30,000 feet and hypersonic speeds.

“These things would be out there all day,” said Lt. Ryan Graves, an F/A-18 Super Hornet pilot who has been with the Navy for 10 years, and who reported his sightings to the Pentagon and Congress. “Keeping an aircraft in the air requires a significant amount of energy. With the speeds we observed, 12 hours in the air is 11 hours longer than we’d expect.”

In late 2014, a Super Hornet pilot had a near collision with one of the objects, and an official mishap report was filed. Some of the incidents were videotaped, including one taken by a plane’s camera in early 2015 that shows an object zooming over the ocean waves as pilots question what they are watching.

“Wow, what is that, man?” one exclaims. “Look at it fly!”

No one in the Defense Department is saying that the objects were extraterrestrial, and experts emphasize that earthly explanations can generally be found for such incidents. Lieutenant Graves and four other Navy pilots, who said in interviews with The New York Times that they saw the objects in 2014 and 2015 in training maneuvers from Virginia to Florida off the aircraft carrier Theodore Roosevelt, make no assertions of their provenance.

Joseph Gradisher, a Navy spokesman, said the new guidance was an update of instructions that went out to the fleet in 2015, after the Roosevelt incidents.

“There were a number of different reports,” he said. Some cases could have been commercial drones, he said, but in other cases “we don’t know who’s doing this, we don’t have enough data to track this. So the intent of the message to the fleet is to provide updated guidance on reporting procedures for suspected intrusions into our airspace.”

The sightings were reported to the Pentagon’s shadowy, little-known Advanced Aerospace Threat Identification Program, which analyzed the radar data, video footage and accounts provided by senior officers from the Roosevelt. Luis Elizondo, a military intelligence official who ran the program until he resigned in 2017, called the sightings “a striking series of incidents.”

Leon Golub, a senior astrophysicist at the Harvard-Smithsonian Center for Astrophysics, said the possibility of an extraterrestrial cause “is so unlikely that it competes with many other low-probability but more mundane explanations.” He added that “there are so many other possibilities — bugs in the code for the imaging and display systems, atmospheric effects and reflections, neurological overload from multiple inputs during high-speed flight.”

Lieutenant Graves still cannot explain what he saw. In the summer of 2014, he and Lt. Danny Accoin, another Super Hornet pilot, were part of a squadron, the VFA-11 “Red Rippers” out of Naval Air Station Oceana, Va., that was training for a deployment to the Persian Gulf.

Lieutenants Graves and Accoin spoke on the record to The Times about the objects. Three other pilots in the squadron also spoke to The Times about the objects but declined to be named.

Lieutenants Graves and Accoin, along with former American intelligence officials, appear in a six-part History Channel series, “Unidentified: Inside America’s U.F.O. Investigation,” to air beginning Friday. The Times conducted separate interviews with key participants.

The pilots began noticing the objects after their 1980s-era radar was upgraded to a more advanced system. As one fighter jet after another got the new radar, pilots began picking up the objects, but ignoring what they thought were false radar tracks.

But he said the objects persisted, showing up at 30,000 feet, 20,000 feet, even sea level. They could accelerate, slow down and then hit hypersonic speeds.

Lieutenant Accoin said he interacted twice with the objects. The first time, after picking up the object on his radar, he set his plane to merge with it, flying 1,000 feet below it. He said he should have been able to see it with his helmet camera, but could not, even though his radar told him it was there.

A few days later, Lieutenant Accoin said a training missile on his jet locked on the object and his infrared camera picked it up as well. “I knew I had it, I knew it was not a false hit,” he said. But still, “I could not pick it up visually.”

At this point the pilots said they speculated that the objects were part of some classified and extremely advanced drone program.

But then pilots began seeing the objects. In late 2014, Lieutenant Graves said he was back at base in Virginia Beach when he encountered a squadron mate just back from a mission “with a look of shock on his face.”