Alison Hernandez, the Devon and Cornwall police and crime commissioner, said she was interested in having a conversation with the chief constable about whether ordinary people with gun licences could assist in a terrorist crisis.
The comments caused alarm within the force and prompted a stern warning from a senior officer that citizens should not arm themselves, The Guardian reported.
Hernandez, a former Conservative election agent, made her comments during an extraordinary exchange with a caller to a phone-in programme on BBC Radio Cornwall.
Hernandez replied that it was a "a very good question" and asked the woman if she would put it in writing so that the chief constable, Shaun Sawyer, could consider it.
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But she then said, "This might be some of our solution to our issues."
When challenged by the presenter if she was advocating vigilantism, Hernandez replied, "I'm just saying, let's officially have a look at that and see what would be the implications of it. Let's unpick it a little bit."
The presenter said he could not believe the chief constable would entertain the idea of the public defending themselves with firearms.
Hernandez said, "I'm sure he wouldn't want to entertain it, but these are times that are challenging and I would like to have an official response on that myself."
Her comments come just days after a suicide bombing at a concert in Manchester claimed 22 lives and an attack at the London Bridge by three terrorists, who drove a van into pedestrians and then went on a stabbing spree, killed eight persons.
"During these incidents, highly trained police firearms officers and special forces will be deployed to protect our communities," Netherton said.
"Under no circumstances would we want members of the public to arm themselves with firearms, not least because officers responding would not know who the offenders were, and quite obviously they would not have the time to ask. Our message to the public is a simple one: to run, to hide and to tell," he added.