A flurry of messages on Twitter using the hashtags #TroyDavis and #TooMuchDoubt showed thousands of supporters of Davis were intent on flooding the Jackson District Attorney's Office, Georgia Judge Penny Freezeman's office, and the U.S. Attorney General's Office with phone calls and e-mails to beg for a stay on the execution.
Some users accused Twitter of blocking the topic from trending on Tuesday, though a representative from Twitter told ABC News there was no such action taken. The hashtags were trending today in cities around the U.S. as well as Germany, the U.K., Sweden and France. Many tweets called the case a symbol of a return to Jim Crow laws and racial inequalities in the justice system.
Big Boi, a member of the group Outkast, tweeted to his followers to go to the Georgia state prison in Jackson to protest the decision. The Roots' Questlove tweeted a similar message.
The NAACP and the Revs. Al Sharpton and Jesse Jackson held a news conference today calling for the execution to be halted.
Amnesty International, which has been fighting on behalf of Davis, encouraged supporters to attend a vigil at the church across the street from the prison at 5:30 p.m. and a protest at 6 p.m., and asked participants to wear a black armband and write on it, "Not in my name!"
Wendy Gozen Brown, a spokeswoman for Amnesty International, said that Davis would want the protests to remain peaceful.
"In this type of situation, there's always the potential for it to go awry, with certain groups, angry rhetoric," Brown said. "But Troy Davis would want people to keep fighting peacefully, for him and for, as he would put it, all of the other Troy Davises out there."
Others who have voiced support for Davis include former President Jimmy Carter, the pope and a former FBI director.
Davis's execution was stayed four times for appeals since his conviction in 1991, and the Supreme Court gave him a rare chance to prove his innocence last year, but rejected his plea.
A Georgia board of pardons and paroles rejected Davis's plea for clemency on Tuesday.
ABC News' Arianne de Vogue and Steve Osunsami and The Associated Press contributed to this report.