Kelly Osbourne -- Giuliana Rancic Better Make It Right with Zendaya ... Or I'll Quit!! [UPDATE]

Kelly Osbourne just dropped an ultimatum on Giuliana Rancic and their "Fashion Police" bosses -- issue a mea culpa for saying Zendaya smells like a hippie pot smoker ... or she'll quit the show.

Kelly is responding to the firestorm Giuliana sparked with a comment about the Disney star's Oscar look -- which included new dreadlocks. Rancic said she thought Zendaya must smell like patchouli oil or weed. Kathy Griffin joined in on the "weed" comment.

Kelly went off on a Twitter rant, saying ... "I'm giving everyone involved 24 hours to make it right or the world will hear how I really feel." She added she doesn't condone racism and is seriously questioning staying on the show.

Osbourne reminded fans she's friends with Zendaya -- who herself blasted Rancic for making such an "outrageously offensive" stereotypical comment.

It sounds like no one involved is buying Giuliana's claim her remarks "had NOTHING to do with race."

4:30 PM PT-- Looks like Kelly has pull ... Giuliana just apologized again -- this time on the air during "E! News."