Italy's ANSA news agency reported 12 demonstrators had tried to force their way in but were stopped at the entrance.
Sources said they were members of a Milan-based group of Syrian nationals who oppose Assad's regime.
In recent days, activists have converged on Syrian embassies in Britain, Germany, Egypt, Greece and Kuwait and the United States closed its embassy in Damascus.
Several other European countries have called their ambassadors home.
At least 7,100 people, including 461 children, have died since the Syria uprising began in March, the Local Coordination Committees, a network of opposition activists, has said. The United Nations said in January 5,400 people had been killed but stopped counting, saying it was too difficult to confirm the toll.
Notable deaths of 2014 [PHOTOS]