An elderly man accused of killing three people outside Jewish sites in Kansas has been identified as a former Ku Klux Klan chief.

A Johnson County official named the suspect as Frazier Glenn Cross.

Public records show that the Cross, 73, also goes by the last name Miller. The Southern Poverty Law Centre says he has long been an outspoken white supremacist and was once a "grand dragon" of the Carolina Knights of the Ku Klux Klan.

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The group reports on its website that it spoke to Miller's wife, Marge, by phone and she said police told her that her husband had been arrested for yesterday's attacks in Overland Park, near Kansas City.

The gunman's deadly rampage happened outside a Jewish community centre and nearby retirement community.

Overland Park police chief John Douglass said the attacks occurred minutes apart. "Today is a sad and very tragic day," he said.

US president Barack Obama, who offered condolences to the families of those killed, said reports of the shooting were "heartbreaking".

Shots were fired behind the Jewish Community Centre of Greater Kansas City in a car park at about 1pm local time. One man died at the scene and another died at a hospital.

The gunman then fled and opened fire at nearby Village Shalom, killing a woman, before being arrested near a primary school. Two other people were shot at, Mr Douglass said.

Family members identified two of the victims as Dr William Corporan and his grandson, Reat Underwood, 14. The family is Christian.

Mr 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". He also said it was too early in the investigation to determine whether there was an anti-Semitic motive for the attacks or if they would be investigated as hate crimes. The Jewish festival of Passover begins today.

Mr Douglass said the suspect was a white man in his 70s who was not from Kansas.

"We have no indication he knew the victims," he said, adding that he was not known to Kansas City authorities before the shootings. Mr Douglass said a shotgun was used and investigators were trying to determine whether a handgun and assault-style rifle were also involved.

The Jewish Community Centre of Greater Kansas City said on its Facebook page that a "shooting incident" happened near its White Theatre entrance.

Kristy Straeb, 47, said her sister-in-law Stacie Ventimiglia was at the centre's pool with a friend and four little girls under seven for a swimming lesson.

"They had just gotten the four babies naked, and somebody yelled into the family locker room, 'We have an active shooter situation. You need to get safe'," Ms Straeb said.

The women got into a cubby area and were "ready to push the little girls into four empty lockers". Ms Straeb said the women and their children were not harmed.