Scamwatch posted a tweet today saying people had been receiving phone calls with automated messages that pretended to inform the listener of a problem.
The listener is instructed to "dial 1" to speak to somebody who can solve the purported issue.
Scamwatch instead said people should hang up.
"It might claim you'll be arrested, that your NBN will be cut off, or that you owe money," Scamwatch said.
"This is a lie designed to scare you into action."
People can report scams at the Scamwatch website.