A white supremacist who shot and killed three people outside two Jewish centres last year should be put to death, a jury in Kansas has concluded.

The jury convicted 74-year-old Frazier Glenn Cross last week of capital murder for the April 2014 shootings. The judge overseeing the trial will now decide whether to follow the jury's sentencing recommendation.

Cross, who raised his arm in a Nazi salute after he was convicted, represented himself at the six-day trial. When presenting his defense, the Missouri man said prosecutors had “a slam dunk.” He then told the jurors: “You guys are going to put me on death row. We all know that.”

Cross admitted killing William Corporon, 69, and Corporon's 14-year-old grandson, Reat Griffin Underwood, at the Jewish Community Center in Overland Park. He also said he shot Terri LaManno, 53, shortly afterward at the nearby Village Shalom retirement center. None of the victims was Jewish.

In a rambling, hour-long closing argument earlier Tuesday, Cross touched on the media, white supremacism and his health. He concluded by telling the jury he didn't care what sentence they handed down.

“Frankly my dears, I don't give a damn,” he said, and again raised his right arm in the Nazi salute.

Cross has said he was suffering from chronic emphysema and wanted to kill Jewish people before he died. A doctor testified during trial that Cross likely had five to six years left to live.

Among Cross' witnesses, was his 39-year-old son, Frazier Glenn Miller III, who testified he doesn't know where his father learned about “hating Jews and about hating other races.”

Cross, a Vietnam War veteran, founded the Carolina Knights of the Ku Klux Klan in his native North Carolina and later the White Patriot Party. He also ran for the U.S. House in 2006 and the U.S. Senate in 2010 in Missouri, each time espousing a white-power platform.

Kansas has not executed a death row inmate since reinstating the death penalty in 1994.