Franklin also killed Ted Fields, 20, and David Martin, 18, in Salt Lake City in August 1980 as the two black men left Liberty Park with two white female friends. Franklin was given a total of four life sentences for the murders after being found guilty in separate federal and state court trials.
Franklin has said the killings were motivated by his hatred of Jews and "race mixing" of African-Americans and whites.
The Utah case helped law enforcement officials connect Franklin to sniper shootings in nine other states between 1977 and 1980, including attacks on civil rights leader Vernon E. Jordan in Fort Wayne, Ind., and "Hustler" magazine publisher Larry Flynt in Lawrenceville, Ga. Both men were wounded but survived the shootings, though Flynt was left paralyzed below the waist.
Franklin has been convicted of, or confessed to, at least 21 killings, 16 bank robberies and two bombings.
Last week, the ACLU of Missouri filed a motion on behalf of Flynt objecting to the state's refusal to disclose information about the compounding pharmacy providing the drug that will be used to carry out the lethal injection or the doctor administering it.
The NAACP opposes the death penalty and considers doing away with it a "major priority."
In her letter, Williams said the NAACP "realizes the crimes committed by Joseph Paul Franklin were based on his hatred toward blacks and Jews and knows the families that were his victims in Utah."
Despite that, Williams told Nixon, there are far better uses for the money the state will spend to end Franklin's life.
"The money saved," Williams wrote, "could be used for services for crime victims and their families and would be beneficial to educational, after-school, public safety, drug and alcohol treatment and child-abuse-prevention programs as well as mental health services and a host of other initiatives."