"Rue was a close and dear friend. I treasure our relationship," White, 88, said in a statement. "It hurts more than I ever thought it would, if that's even possible."
McClanahan died early Thursday at age 76 after suffering a stroke, following the deaths of costars Bea Arthur last year at age 86 and Estelle Getty in 2008 at age 84 .
Golden Girls producer and writer Marc Cherry also expressed sadness over McClanahan's death.
"When I worked on The Golden Girls, my favorite character to write for was Blanche Devereaux," he said. "In the hands of lesser actresses Blanche's vanity and sexual appetite would have been off-putting. But in Rue's brilliant hands, that character became one of the most beloved in the history of TV.
"Rue's kindness, generosity and enormous talent will be sorely missed."