RALEIGH — North Carolina Gov. Roy Cooper and public health officials unveiled on Tuesday a new alert system that will encourage counties with high levels of coronavirus transmission to more aggressively enforce statewide health guidelines and punish noncompliant businesses.

Dangled over the counties’ heads is a big stick: the possibility of the state placing greater restrictions on them.

Leaders in over half of the state’s counties, including 10 deemed to have “critical community spread,” are now being encouraged to pass ordinances levying fines against residents and businesses not complying with public health directives. They include the statewide mask mandate Cooper enacted months ago to combat COVID-19, as well as gathering limits.

The 10 “critical” counties, mainly in rural areas, and 44 others with “substantial” spread also are being asked to consider cutting off alcohol sales earlier than the current 11 p.m. deadline statewide. And churches in those counties are advised not to hold any indoor in-person gatherings of more than 10 people.

The Democratic governor warned of further restrictions if counties don’t heed the state’s advice.

“We may have to do more even on a statewide level or at a local level in some way,” Cooper said at a news conference. “That decision has not yet been made, but we are hoping that this effort can help us slow the spread.”

Cooper noted people are still able to travel freely throughout the state.

“We want to work with these counties to see if we could lower the spread with the recommendations that we have in place now,” Cooper said. “Right now, those recommendations don’t include travel restrictions.”

The new alert system assigns a color to counties based on the rate of cases, the percentage of coronavirus tests coming back positive and a score given based on how local hospitals are faring with COVID-19 patients and staffing shortages. Counties in yellow are seeing significant community spread, while those in orange are seeing substantial spread and those in red have critical spread.

Cooper said North Carolina isn’t faring as badly as other states, though cases, hospitalizations and positivity rates are seeing some of their highest levels yet. The state on Tuesday reported a single-day increase of 3,288 COVID-19 cases, which is its second-highest daily count since the pandemic began. More than 1,500 patients are currently hospitalized with coronavirus symptoms.

“What we’re trying to do is reenergize the people of our state,” Cooper said.