County Commissioner Tim Boyd said Mayor Andy Berke should put a curfew in place.
Commissioner Boyd said, "I think you need to turn your focus away from the C-19 pandemic and place a higher priority on the unrest taking place on the streets of our city.
"Put in place a curfew now before more folks are injured and/or arrested not to mention the potential for more property damage."
The Chattanooga mayor earlier strongly condemned the death of George Floyd in Minneapolis.
He has had no comment after two nights of unrest and multiple arrests in Chattanooga except to say on Sunday night, “We encourage everyone in Chattanooga to exercise their First Amendment rights and express themselves in a safe way.”
On Sunday night, someone left messages with chalk outside the mayor's home, WRCB reported. There were chalk outlines of bodies as well as profanity toward the police and the phrase "I can't breathe."
Chattanooga Police placed a patrol car with an officer inside in front of the mayor's home. The station said at one point he and his dog came outside and he gave a treat to the officer.