Investigators continue to collect evidence, and while there are no suspects yet, police are "possibly talking to a person of interest," Greenville Police Chief Delando Wilson said at the news conference.
Authorities are treating the act as a hate crime, he said, because it's viewed as an attempt to intimidate voters.
"It tries to push your beliefs on someone else, and this is a church, a predominantly black church, and no one has a right to try and ... pressure someone into the way they want to decide to vote in this election," the chief said.
The west Mississippi city of about 33,000 located near the Arkansas border is 78% black, according to the most recent census. Surrounding Washington County is 71% black.
Mayor Errick Simmons said he spoke to some of the church's 200 congregants who were fearful and felt intimidated. They felt the vandalism was not just an attack on the church, but on the black community, he said.