Police said the attacks at both sites happened outside and the gunman never entered any buildings. Douglass said the gunman also shot at two other people during the attacks, but missed.
Authorities declined to release the victims' names pending notification of their relatives. However, the family of the first two victims released a statement identifying them as Dr. William Lewis Corporon, who died at the scene, and his 14-year-old grandson, Reat Griffin Underwood, who died at Overland Park Regional Medical Center.
They were both Christian, and the family thanked members of their church congregation, among others, for their support.
"We take comfort knowing they are together in Heaven," the family said. It asked for privacy to mourn.
Rebecca Sturtevant, a hospital spokeswoman, said family members told her Corporon had taken his grandson to the community center so that the boy could try out for a singing competition for high school students. Reat was a freshman at Blue Valley High School 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 in the small southwest Missouri town of Aurora, some 180 miles south of Overland Park. A red Chevrolet adorned with Confederate flag stickers was parked outside. An AP reporter knocked on the front door of the house early Monday, but no one answered.
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 and told her that her husband had been arrested in Sunday's attacks.