Douglass said the suspect made several statements to police, "but it's too early to tell you what he may or may not have said" during the attacks. He also said it was too early in the investigation to determine whether Cross had an anti-Semitic motive. The Jewish festival of Passover begins Monday evening.
"We haven't ruled out anything," he said.
Attorney General Eric Holder said federal prosecutors will investigate whether the killings were a hate crime. Justice Department attorneys and the FBI planned a midday news conference. It wasn't clear when Cross would make a court appearance or face formal charges.
SITE, a U.S.-based terror monitoring group, described the suspect as a known and vocal anti-Semite who frequently calls for genocide against Jews.
Police said the attacks happened within minutes of one another. At around 1 p.m. a gunman shot two people in the parking lot behind the Jewish Community Center of Greater Kansas City. He then drove a few blocks to a retirement community, Village Shalom, and gunned down a woman or girl there, Douglass said. Officers arrested him in an elementary school parking lot soon after.
Douglass said the gunman shot at but missed two other people. Police said the gunman never entered any buildings.
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. The family thanked the church and others for their support.
"We take comfort knowing they are together in Heaven," the family said, requesting privacy to mourn.
Rebecca Sturtevant, a hospital spokeswoman, said family members told her Corporon took his grandson to the community center to try out for a high school students' singing competition. 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 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 and told her that her husband had been arrested in Sunday's attacks.
The law center said the suspect has been involved in the white supremacist movement for most of his life. He founded the Carolina Knights of the Ku Klux Klan and was its "grand dragon" in the 1980s. The Army veteran and retired truck driver later founded another white supremacist group, the White Patriot Party, the center said.
He was the subject of a nationwide manhunt in 1987 for violating the terms of his bond while appealing a North Carolina conviction for operating a paramilitary camp. The search ended after federal agents found him and three other men in an Ozark mobile home, which was filled with hand grenades, automatic weapons and thousands of rounds of ammunition. He ran for U.S. House in 2006 and the U.S. Senate in 2010, espousing a white power platform.
SITE said Monday that the suspect is a prominent member of the Vanguard News Network and has posted thousands of messages including frequent calls for genocide against Jews on the neo-Nazi forum's website. His most recent post was Saturday.
Associated Press writer Tim Jacobs in Chicago; Pete Yost in Washington; and Katarina Kratovac in Cairo contributed to this report.