The body of the first slain officer was found near a stadium where Greene, who is white, was expelled by police last month after waving a Confederate battle flag in front of black spectators.
Four Confederate flags were placed overnight at Ebenezer Baptist Church and the MLK Visitor Center in Atlanta.
At least five people were arrested on Saturday as white-supremacist and African-American groups clashed outside the South Carolina State House, where the Confederate battle flag was removed last week after a half-century, authorities said.
Governor Nikki Haley (R) hopes that South Carolinians will simply ignore "the disruptive, hateful spectacle members of the Ku Klux Klan hope to create."
Donald Trump is railing against immigrants trying to get into the country, meanwhile we've got conservative activists and officers of the court angling to get out. Misogyny, paranoia, xenophobia, oh my!
South Carolina governor Nikki Haley announced that the Confederate flag will be removed from the State House grounds on July 10.