A Facebook group calling itself The Syrian Revolution 2011 called for a "Day of Rage" for Friday in the spirit of the Tunisian and Egyptian revolutions.
The group had the support of more than 10,000 fans but protests didn't develop despite the outpouring of support on the Internet, al-Jazeera reports.
Syrian President Bashar Assad said in an interview published this week by The Wall Street Journal that he saw a new era developing in the Middle East as the Tunisian, Egyptian, Jordanian, Yemeni and Algerian governments felt the pressure from anti-government demonstrators.
Assad has moved relatively closer to the West in the wake of the U.S.-led invasion of Iraq.
Human Rights Watch complained that a small group of people dressed in civilian clothes beat about a dozen protesters who gathered in Damascus in a show of solidarity for Egyptian demonstrators.
Sarah Leah Whitson, the Middle East and North Africa director for Human Rights Watch, said the Syrian government was using "thugs" to attack peaceful protesters.
"President Bashar Assad seems to have taken a page out of the rulebook of his Egyptian counterpart," she said in a statement.