RIYADH, Saudi Arabia—A 23-year-old Saudi columnist fled the country, his associates said Wednesday, after his tweets on the human nature of the Prophet Muhammad led prominent clerics and thousands of their followers to use Twitter, YouTube, email and fax to demand the writer's execution.

The speed, number and intensity of messages calling for the death of the writer, Hamza Kashgari, stunned many Saudis.

"Your...