Residents and business owners are complaining about disruptive behavior, which they say is scaring tourists.
The complaints include at least one report of a homeless person snatching a customer's food from an outdoor table on River Street, Savannah Mayor Edna Jackson said at a Thursday city council meeting.
Mayor Pro Tem Van Johnson, who represents downtown, and Alderman Tony Thomas also said they were hearing from constituents about additional concerns.
Residents say they're worried about public urination, belligerent demands for money and the use of downtown squares and park benches for sleeping, The Savannah Morning News reported.
Vagrants are rummaging in trash cans for food or are congregating in a plaza near the ferry launch, which can be intimidating to visitors to Savannah, according to business operators along River Street.
"We're a tourist town," said Denise Scott, who manages Washed Ashore, a clothing and accessories shop. "You don't want to see a bunch of homeless people asking you for money. It just doesn't look good."
Nick Pappas, owner of the Olympia Cafe, says tourists have been fearful.
"People come here and they see these people traveling with dirty dogs or pushing flowers at them, and the tourists don't want to come out at night," he said. "They're afraid to take out their wallets on the street. We need to clean up our act. It's getting worse by the day."
Police Chief Willie Lovett planned to meet with concerned downtown business leaders, and he said they're developing a response plan.