Campaigns on Facebook and Twitter have called for a "day of rage" in Damascus on Friday and Saturday.
The campaigns take inspiration from Egypt and Tunisia in using social networking sites to rally their followers for sweeping political reforms.
Syria's authoritarian president has resisted calls for political freedoms and jailed critics of his regime.
By early afternoon, no protesters had gathered outside Syria's parliament.
Human Rights Watch quotes witnesses as saying Syrian security forces have been intimidating people in recent days who have tried to assemble to support the protesters in Egypt.