'Good Will Hunting' actor Robin Williams committed suicide by cutting his wrist before hanging himself with a belt on August 11. He was 63.
Zelda also received abusive messages from the two, reported Contactmusic.
She first urged her followers to report the trolls, before announcing she was taking a break from the social media site, possibly forever.
She wrote in a tweet which she then deleted: "Please report PimpStory MrGoosebuster. I'm shaking. I can't. Please. Twitter requires a link and I won't open it. Don't either. Please (sic)," she wrote on the micro-blogging site.
"I'm sorry. I should've risen above. Deleting this from my devices for a good long time, maybe forever. Time will tell. Goodbye," her next tweet read.
The two users' accounts have now been suspended.