WASHINGTON — If the truth is out there, it certainly is not apparent yet.

Pentagon and intelligence officials are trying to make sense of three unidentified flying objects over Alaska, Canada and Michigan that U.S. fighter jets shot down with missiles on Friday, Saturday and Sunday.

The latest turn in the aerial show taking place in the skies above North America comes after a helter-skelter weekend involving what at times seemed like an invasion of unidentified flying objects.

The latest object had first been spotted on Saturday over Montana, initially sparking debate over whether it even existed. On Saturday, military officials detected a radar blip over Montana, which then disappeared, leading them to conclude it was an anomaly. Then a blip appeared Sunday over Montana, then Wisconsin and Michigan. Once military officials obtained visual confirmation, they ordered an F-16 to shoot it down over Lake Huron.

There are two big questions around the episodes: What were the craft? And why does the United States appear to be seeing more suddenly, and shooting down more?

There are no answers to the first question yet. American officials do not know what the objects were, much less their purpose or who sent them.

For the second, it is not clear if there are suddenly more objects. But what is certain is that in the wake of the recent incursion by a Chinese spy balloon, the U.S. and Canadian militaries are hypervigilant in flagging some objects that might previously have been allowed to pass.

After the transit of the spy balloon this month, the North American Aerospace Defense Command, or NORAD, adjusted its radar system to make it more sensitive. As a result, the number of objects it detected increased sharply. In other words, NORAD is picking up more incursions because it is looking for them, spurred on by the heightened awareness caused by the furor over the spy balloon, which floated over the continental United States for a week before an F-22 shot it down on Feb. 4.

“We have been more closely scrutinizing our airspace at these altitudes, including enhancing our radar, which may at least partly explain the increase in objects that we’ve detected over the past week,” Melissa Dalton, the assistant secretary of defense for homeland defense and hemispheric affairs, said at a news conference on Sunday evening.

American officials have not completely discounted theories that there could also be more objects, period. Some officials theorize that the objects could be from China, or another foreign power, and may be aimed at testing detection abilities after the spy balloon.

The object spotted approaching Lake Huron on Sunday was flying at 20,000 feet and presented a potential threat to civil aviation, so President Biden ordered it shot down, U.S. officials said. It had an octagonal structure with strings hanging off but had no discernible payload, they added.

U.S. and Canadian officials say the objects shot down on Friday and Saturday were also flying lower than the spy balloon, posing a greater danger to civilian aircraft, which prompted leaders to order them destroyed. Those two objects were flying over parts of Alaska and the Yukon that have few residents, and the third object downed on Sunday was over water, so risks posed by falling debris were minimal, they said.

The spy balloon that drifted across the United States flew much higher, at 60,000 feet, and did not pose a danger to aircraft. But any falling debris could have hit people on the ground, Pentagon officials said.

Throughout the weekend, officials said they were still trying to determine what the three objects were. The first, a Defense Department official said, is most likely not a balloon — and it broke into pieces after it was shot down on Friday. Saturday’s object was described by Canadian authorities as cylindrical, and American officials say it is more likely it was a balloon of some kind. Sunday’s object appeared unlikely to be a balloon, one official said.

NORAD radar tracked the first two objects for at least 12 hours before they were shot down. But Defense Department officials have never said whether they picked the objects up on radar before they neared American airspace. One official said it is unclear what keeps the objects aloft.

U.S. officials said they are reviewing video and other sensor readings collected by the American pilots who observed the objects before their destruction. But the exact nature of the objects, where they are from and what they were intended for will not be confirmed until the F.B.I. and the Royal Canadian Mounted Police have the chance to thoroughly examine the debris, officials said.

Asked during a news conference on Sunday whether he had ruled out extraterrestrial origins, Gen. Glen D. VanHerck, the commander of the Air Force’s Northern Command, said, “I haven’t ruled out anything at this point.” But in interviews Sunday, national security officials discounted any thoughts that what the Air Force shot out of the sky represented any sort of alien visitors. No one, one senior official said, thinks these things are anything other than devices fashioned here on Earth.

Luis Elizondo, the military intelligence officer who ran the Pentagon’s U.F.O. program until 2017, concurred. But he said that the Biden administration must find a way to balance vigilance over what is going on in the skies above America against “chasing our tail” whenever something unknown shows up — a tough task, he said.

For years, adversaries have sent low-tech gadgets into the skies above the United States, Mr. Elizondo said.

“What’s happening now is you have low-end technology being used to harass America,” he said in an interview. “It is a high-impact, low-cost way for China to do this, and the more you look up in the sky, the more you will see.”

At the urging of Congress, the Pentagon and intelligence agencies have intensified their study of unexplained incidents near military bases in recent years. The studies on what the intelligence community calls unidentified aerial phenomena have pinpointed previously undetected efforts to conduct surveillance on American military exercises and bases. Many of those unexplained incidents have been balloons, and some of them are now believed to be attempted surveillance activity by China or other powers, both using balloons and surveillance drones.

“We can now assess flight patterns and trajectory in a much more scientific way,” said Senator Kirsten Gillibrand, a New York Democrat who wrote the recent legislation mandating greater internal military reporting and analysis of aerial phenomena, leading to more documentation of sightings. “You need to know who’s using the technology and what it is.”

The most alarming theory under consideration by some U.S. officials is that the objects are sent by China or another power in an attempt to learn more about American radar or early warning systems.

A senior administration official said one theory — and the person stressed that it is just a theory — is that China or Russia sent the objects to test American intelligence-gathering capabilities. They could be sent to learn both how quickly the United States becomes aware of an intrusion and how quickly the military can respond to such an incursion, the official said.

American officials are united in their belief that the spy balloon that transited the United States was a Chinese machine meant to conduct surveillance on American military bases. Officials said it was unclear if China had complete control of the balloon during its whole journey. But officials said China did have at least a limited ability to steer it, and the balloon maneuvered on Feb. 3 before it was shot down the next day.

Another American official said the Chinese spy balloon was equipped with a self-destruct mechanism, but Beijing did not use it, a potential sign that Chinese officials wanted to continue to collect intelligence, even after it was discovered.

The disclosure of the balloon by the Pentagon on Feb. 2 led to a public diplomatic crisis between China and the United States. Beijing said it had the right to respond further. On Sunday, a Chinese newspaper reported that local maritime authorities in Shandong Province on the east coast had spotted an “unidentified flying object” in waters by the city of Rizhao and were preparing to shoot it down. State-run news organizations reposted the information.

If any of the devices destroyed in North America over the past three days were Chinese, it would amount to a major provocation on the heels of the spy balloon, one reason some officials said not to jump to the conclusion that the objects are surveillance devices sent from Beijing.

Officials in Beijing seem to want to limit tensions over the spy balloon, suggesting to some U.S. officials that the latest objects are less likely to be deliberate Chinese provocations or tests.

Pentagon officials have been raising flags about deficiencies in North America’s aging warning systems, radar and sensors.

Speaking last year at the Aspen Security Conference in Colorado, General VanHerck said that the United States had struggled to detect certain intrusions, what he called “domain awareness challenges.” General VanHerck said the NORAD radars could not adequately detect hypersonics and other threats.

But, he also said, the United States and Canada were investing in new over-the-horizon radar to better identify potential threats, as well as artificial intelligence systems to help pick out possible intrusions.

“I’m very encouraged with where we’re going,” General VanHerck said last July, “but we still have some challenges to work on.”

Claire Fu contributed reporting from Seoul.