McClanahan died Thursday of a massive stroke. She was 76.
"Rue was a close and dear friend. I treasure our relationship," White said in a statement issued to People.com. "It hurts more than I ever thought it would, if that's even possible."
White is now the only surviving cast member of the 1980s senior-themed sitcom "The Golden Girls." Bea Arthur died last year at the age of 86 and Estelle Getty in 2008 at 84.