Bristol City Council plans to re-write its approach to graffiti in the city, which is known internationally for its street art.
Assistant Mayor Daniella Radice said Bristol's reputation was attracting taggers from outside the area.
Police believe more than 80 people are what it called "actively offending" in the area.
Ms Radice said she wanted to recognise "the contribution that street art can make, while opposing tagging".
Bristol is known for its connections to street artist Banksy - the city's tourism body promotes walking tours of his murals - and is also home to Upfest, an international street art festival which is taking place in Bedminster and Southville this weekend.
But Green Party councillor Ms Radice told BBC Radio Bristol: "Because we are a city that's celebrated for our street art... people think if they come and tag here, maybe they will get some extra recognition for it."
She wanted to "re-write" the existing policy to help make it clearer "what we think is art and what we think is not", to include strict enforcement against tagging while supporting "street art".
She said more "legal walls" might be needed - currently there is one in a park near junction 3 of the M32 - and more resources might be needed to help communities and businesses clean up tagging.
Avon and Somerset Police have been running "Operation Block" alongside the council - targeting illegal graffiti and "tagging" - where people spray their signatures onto walls.
Last month a man from Bournemouth received a suspended sentence after admitting 78 counts of criminal damage in the city while another man from York admitted causing damage at 15 locations.