Councillor Peter Scott of Newport said: "I am hearing concerns from worried residents about a lack of care on social distancing, poor queuing behaviour and some not wearing masks appropriately in the High Street.
"If you stop to chat please keep your distance.
"Remember Newport North and West is a high risk area currently.
"Please follow the guidance – let's get our numbers down, let's keep each other safe."
He reminded people that wearing masks is mandatory inside shops.
On the Government's online coronavirus case tracker, which can be viewed at coronavirus.data.gov.uk/details/interactive-map, Newport town is split into 'Newport north' and 'Newport south'.
For the seven days to January 6, these two areas had 31 and 32 cases respectively according to the tracker.