The European Union has imposed an arms embargo on Syria as well as an asset freeze and visa ban on 13 top Syrian officials.
The president's younger brother Maher al-Assad tops the EU list.
He is described as the principal overseer of violence against demonstrators.
President Bashar al-Assad is not included. But the EU says he too could face sanctions if he fails to end the crackdown.
Human rights groups say hundreds of civilians have been killed in the unrest.
The demonstrations calling for political reform began in mid-March.
Authorities say they are combating an armed insurrection by what they call gangs of terrorists.