Issuing a renewed public appeal for information, Area Inspector Constantine said: “I want to reassure the public that incidents like this are rare, they will not be tolerated and will be dealt with robustly.
“Horncastle is a lovely area to live and work and the community at large are shocked and disgusted at the nature of these comments, which in no way represent the views of the community.
“I am hoping that the community will be able to provide some information to identify those responsible so that the police can take appropriate action.”
The incident - which is being treated as a hate crime due to the racist language - was reported to Lincolnshire Police last Thursday morning (June 28) after the graffiti appeared on the side of various buildings in the town centre overnight.
Police have been conducting house-to-house enquiries and assessing CCTV opportunities since then.
Patrols have been increased in the area, although no suspects have been identified at this stage.
Meanwhile, Horncastle Mayor Brian Burbidge has also condemned those responsible for the graffiti, and praised the ‘community spirit’ of those who offered to help remove the damage last week.