Over the weekend 21 penalty notices were issued for breaches of the ‘rule of six’.
On Monday, a further 19 were issued.
Police say the vast majority of people are adhering to regulations but those who don't will face consequences.
More Covid-19 coverage:
Superintendent Jim Baker, of West Mercia Police, said: “We know some residents in Newport are concerned that not everyone is adhering to the current Covid-19 regulations, and while we would not want to single out any particular groups, it is really important that everyone plays their part and adheres to the ‘rule of six’.
“The vast majority of people are taking necessary steps and are adhering to the Covid-19 regulations but where there are intentional breaches our approach to enforcement will be robust.
“We know it is difficult for everyone as we adapt to a different way of life, but we all need to do our bit to help protect not just ourselves, but our families and friends.
“Over the coming days we will continue to work with local establishments and the local community in Newport to offer advice and support to ensure everyone is playing their part and adhering to the current regulations.”