The gunman shot at but missed two other people and never entered any buildings, police said.
The victims were identified as Dr. William Lewis Corporon, who died at the scene; his 14-year-old grandson, Reat Griffin Underwood, who died at Overland Park Regional Medical Center; and 53-year-old occupational therapist Terri LaManno, a Catholic who was visiting her mother at the retirement complex near the community center.
All three were Christians.
"We want to express our condolences to the families of these poor souls who happened to be in the wrong place at the wrong time and had the unfortunate experience of a firsthand encounter with evil," U.S. Attorney Barry Grissom said.
Rebecca Sturtevant, a hospital spokeswoman, said family members told her Corporon took his grandson to the community center to try out for a student singing competition. Reat was a high school freshman and an Eagle Scout.
Cross is also known as Frazier Glenn Miller. A public records search shows he has used both names, but he refers to himself on his website as Glenn Miller and went by the name Frazier Glenn Miller in 2006 and 2010 campaigns for public office.
Cross lives in a small single-story home bordered on three sides with barbed wire fences just outside the small southwest Missouri town of Aurora, some 180 miles south of Overland Park. A red Chevrolet bearing two Confederate flag stickers was parked outside.
An AP reporter knocked on the front door of the house early Monday but no one answered.
Neighbor Mitzi Owens, 45, said Cross always seems friendly but that locals are well aware of his racist leanings.
"It's crazy that someone can be so likable but be full of this kind of hate," she said.
The Southern Poverty Law Center, which tracks hate groups, said it reached his wife, Marge, by phone and that she said authorities had been to their home.