Eitzen is in southern Minnesota near the Iowa boarder.
In a lengthy statement, Adamson said his city "in no way supports racism and violence," and said that on September 15 "a concerned citizen" notified city officials when they saw a team of three people in an out-of-state vehicle, knocking on doors "claiming to be conducting a Covid-19 survey and tests."
"In a very small town where everyone knows everyone, a group of unfamiliar people with out-of-state plates is unusual, and to some residents its cause for concern," he said.
Adamson said the Houston County Sheriff's Department came to assess the situation in the presence of city officials and two residents. The sheriff's department confirmed the team was part of the MDH, he wrote.
Huff told WCCO that the survey team was confronted by three men, one of whom was armed, and the team felt intimidated.
"We would like to make it clear there was never a gun or any weapon present, and no threats or aggressive behavior occurred during the interaction between the city members and the Covid-19 team," Adamson said.
It's possible the survey team "misinterpreted a large fire department communication radio in a holster for a firearm," Adamson said in his post.
On Saturday, the sheriff's department told CNN there was nobody who could speak on the matter and to try back on Monday.
The mayor's statement did not address any other incidents that the health department referred to.
CNN Health reached out to the CDC, and has not heard back.