Scores of unidentified drones, flying at night and often in groups, have baffled officials in the neighbouring states of Colorado and Nebraska.
Witnesses have spotted the drones, which reportedly have six-foot (1.8m) wide wingspans, since mid-December.
Local law enforcement officials say they have no idea where the drones are coming from or who is flying them.
The sheriff of Yuma County, Colorado said they were being flown in airspace controlled by the federal government.
A Facebook post from Sheriff Todd Combs on Tuesday described local residents as “very nervous and anxious” and said local agencies planned to meet next Monday to try to solve the mystery.
“There are many theories about what is going on, but at this point, that’s all they are,” the sheriff wrote.
“I think we are all feeling a little bit vulnerable due to the intrusion of our privacy that we enjoy in our rural community, but I don’t have a solution or know of one right now,” he wrote, adding that it is potentially illegal for residents to shoot them down.
Colorado Senator Cory Gardner also weighed in, writing on Twitter that officials from the Federal Aviation Administration (FAA) had told him they have “opened a full investigation to learn the source and purpose of the drones”.
A spokesman for the FAA confirmed to BBC News on Thursday that “multiple FAA division and government agencies are investigating these reports,” but would not comment on the status of the inquiry.
According to witness reports, the drones are typically seen flying between 19:00 and 22:00 local time. They normally stay around 200ft in the air and sometimes fly in tandem with other drones.
Facebook groups have popped up with people devoted to tracking the drones in hopes of discovering their origin or purpose.
Drones are used in several industries in the American West and Great Plains, such as agriculture, oil and gas extraction and construction.
“In terms of aircraft flying at night and not being identified, this is a first for me personally,” Sheriff James Brueggeman of Perkins County, Nebraska told the Washington Post, adding that he had been urging disconcerted residents not to attempt to shoot them.
“I think it’s kind of a joke, but you have to remember the part of the country we live in,” the sheriff said. “People here don’t like their privacy to be invaded.”
Residents say the noise of the drones can be heard far across the plains, and upset livestock and pets.
The FAA has recently proposed a rule that would make it easier for local law enforcement officials to identify drones flying over their jurisdictions.
The rule would require all drones weighing more than .55lb (.25kg) to emit a unique identifier signal. Nearly 1.5 million drones and 160,000 remote operators are currently registered with the FAA.