The posters were identified ahead of a police engagement event in the local community.
Mr Tennyson has said: “These sinister posters are clearly intended to intimidate local residents who wish to engage positively with the PSNI, as well as officers themselves. They must be roundly condemned by all.
“The vast majority of people in Lurgan want to move forward towards a more shared and inclusive future. Those responsible for this campaign do not speak for them, and seek only to drag our community back through fear and division.
“Alliance stands fully in support of the PSNI, its officers and staff, who place themselves at risk every day to protect everyone in our society. We will continue working to support them in their efforts to build a service which is diverse and representative of our entire community.”