The governor of New Jersey has asked residents of the state plagued with unexplained drone sighting to “calm down” as federal and state authorities warned of pilots of manned aircraft being hit in the eyes by laser pointers aimed from the ground.

The FBI and New Jersey state police said in a statement on X: “There is also a concern with people possibly firing weapons at what they believe to be UAS [unmanned aircraft systems] but could be manned aircraft.”

The law enforcement agencies added that they have been out every night to legally track down drone operators “acting illegally or with nefarious intent” and warned that there could be “dangerous and possibly deadly consequences” if manned aircraft are targeted.

The warnings came as the FBI, US homeland security department, Federal Aviation Administration (FAA) and defense department issued a statement that said an examination of “the technical data and tips from concerned citizens” concluded “the sightings to date include a combination of lawful commercial drones, hobbyist drones, and law enforcement drones, as well as manned fixed-wing aircraft, helicopters and stars mistakenly reported as drones”.

“We have not identified anything anomalous and do not assess the activity to date to present a national security or public safety risk over the civilian airspace in New Jersey or other states in the northeast,” the statement said.

Nonetheless, a nervous public in New Jersey and nearby states, with their eyes trained to the night sky, continue to report flying lights. Conspiracy theories about a secret government program, Project Blue Beam, are proliferating even as similar ones about an alien invasion diminish.

Project Blue Beam is a theory introduced by the Canadian journalist Serge Monast in the 1990s that holds global elites will destabilize society by staging and unleashing massive supernatural events – alien invasions, holographic displays of cultural and religious figures, mind-control and faked crises – and then capitalize on the hysteria to implement a new world order.

The name is a likely derivation of Project Blue Book, a US air force program that investigated unidentified flying objects (UFOs) from 1947 to 1969.

The FBI said in the statement that “misidentification often occurs when UAS are mistaken for more familiar objects such as manned aircraft, low-orbit satellites, or celestial bodies like planets and stars”.

The agencies advised residents to use flight, satellite and star-tracking apps to help determine if they are looking at drones, or UAS, “or something else”.

On Monday, the New Jersey governor, Phil Murphy, was asked what message he had for people staring in the sky at night.

“First of all, I’d say calm down,” Murphy said. “There’s no evidence of anything nefarious here. We never say never, but … take a breath.” He also noted that drone sightings had been down in recent days. Rain and cloud has been in the forecast.

The FBI recently said it had received more than 3,000 sightings of alleged drones in the state, with hundreds more in neighboring areas.

The governor also said the federal government had sent three “very sophisticated” radar systems overseen by “really sophisticated individuals” to help solve the mystery after existing equipment proved insufficient.

Get the most important US headlines and highlights emailed direct to you every morning

after newsletter promotion

But Murphy also conceded that “there may be suspicious activity out there as we stand here today, but there is little to no evidence of that right now”, based on what the new systems have detected.

A lack of clarity over the sightings has created a vacuum filled by conspiracy theories. On Monday, President-elect Donald Trump said the government was “keeping people in suspense” and “knows what is happening”.

But the White House, FBI and US Department of Homeland Security has said people were mistaking ordinary aircraft for drones. Nonetheless, Murphy said he understood why people were alarmed.

“I can’t walk out that door and have somebody not stop me and say, ‘Tell me what’s going on with the drones.’ And I get that completely,” the governor added. “It’s unnerving and it’s really when life is not a math problem with X plus Y equals Z where there’s a hard and fast answer.

“I hesitate to use mass hysteria because I think the anxiety is legitimate.”

Murphy conceded the collective anxiety has affected him whenever he has taken his dog out at night. “I’m looking up, and I’m trying to figure out: ‘is it a star?’” Murphy said. “‘Is it an aircraft? What is that?’”

The FBI said in an earlier statement that it had “no evidence at this time that the reported drone sightings pose a national security or public safety threat or have a foreign nexus”. The agency also said it had “uncovered no such malicious activity or intent at this stage”.