The Oregonian newspaper reported it received the letter discussing the killing from David "Joey" Pedersen.
According to the newspaper, Pedersen wrote that he and his girlfriend, Holly Grigsby, were looking for another vehicle to help them stay ahead of the law when they killed Reginald Clark in Eureka, Calif., in early October, just before they were finally caught.
Since their arrest the two white supremacists have given statements and interviews bragging about the crimes they are accused of committing.
In his letter to The Oregonian, Pedersen used white supremacist justifications for the death of Clark. Pedersen wrote he and Grigsby decided to kill a "non-white."
"We felt it'd be optimal if, in securing another vehicle, we could also take some riffraff off the street," Pedersen wrote.
As it turned out, the pair did not take Clark's vehicle. Instead, they kept a car they had stolen from the third victim, 19-year-old Cody Myers of Oregon.
Myers' body was found in Western Oregon on Oct. 4 with gunshot wounds in the head and chest. Pedersen and Grigsby were driving Myers' car when they were arrested Oct. 5 north of Sacramento.
Pedersen did not say why they chose not to take Clark's vehicle.
A message left Friday for Pedersen's attorney, Gil Levy of Seattle, by The Associated Press wasn't immediately returned.
The killing spree began with the deaths of Pedersen's father and stepmother at their home in Everett, Wash., around Sept. 26.
In his letter, Pederson wrote that "everything that Ms. Grigsby and I have done -- that which has been made public and that which hasn't -- was done to facilitate our move south, away from Washington and Oregon and the area in which the manhunt for us was most greatly concentrated."
He said the pair planned to travel to the "first large city" to give them some "breathing room to operate and in which we would have a number of options to choose from when it came to the selection of a target."
The couple's motives in their other alleged crimes aren't clear. They told prosecutors they killed Pedersen's father for abusing two young relatives and killed the stepmother because she knew and still supported him. Police have not verified that story.
Grigsby and Pedersen have sought to portray themselves as warriors on a campaign to -- as Grigsby put it in an interview with a California newspaper -- keep "our race" from "being wiped out."
Grigsby told investigators they killed Myers because the teen's last name made them think he was Jewish. But in a later newspaper interview she said they didn't know his name until they had taken his wallet. Myers was a devout Christian.
In his letter to The Oregonian, Pedersen said he and Grigsby had set out to "strike out as often as possible at various members of the Jewish community here in America."
The pair is being held in Washington state. Both pleaded not guilty Wednesday to two counts of aggravated murder in the death of Pedersen's father and stepmother.
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