Britain, France, Germany and Portugal have drafted the resolution, which condemns President Bashar Assad's government, but does not impose sanctions or authorize military action.
Russia and China have opposed it, without saying if they would use their vetos in the Council to block it.
"The outcome of this resolution is in your hands. It qualifies the repression in Syria as a crime against humanity," the letter addressed to the 15 Security Council members said.
"It does not propose sanctions against Syria nor military intervention. It is limited to condemning the repression and clearing the path for investigations into the crimes against humanity. However limited, this resolution is necessary."
'Tragic and morally unacceptable'
The letter, published on Wednesday on the website of French intellectual and writer Bernard-Henri Levy, is also signed by David Grossman, Amos Oz, Orhan Pamuk and Wole Soyinka.
Levy was instrumental in introducing the Benghazi-based Libyan rebels to French President Nicolas Sarkozy ahead of his decision to intervene against Muammar Gaddafi in March.
"It would be tragic and morally unacceptable if, because of the threat of an eventual veto or the occasional abstention here or there, this proposed resolution not be reviewed only to finish in the bin of abandonment," the letter said.
The letter follows a speech by Assad in which he promised reforms to address a wave of protests against his rule but which opponents said did not meet demands for sweeping political change and which the European Union called "disappointing".
- Follow Ynetnews on Facebook