An influential body of international judges and lawyers called for Mr Assad and his lieutenants to be held to account for Easter weekend attacks in which troops and militamen fire on civilians.
"Those ordering and carrying out these attacks, including those firing live rounds into crowds, must be held criminally accountable," the International Committee of Jurists (ICJ) said in a statement.
As opposition supporters continued to bury dead comrades on Sunday, four more were reported to have been killed.
William Hague, the Foreign Secretary, warned all Britons in Syria that the scale of violence was so grave they should leave immediately or risk not being able to leave "at all" as the turmoil worsened.
Western governments were coming under growing scrutiny for their divergent policies towards Libya and Syria, where more than 300 people have been shot dead since unrest began five weeks ago.
Syria has deployed many of the same tactics used by Col Gaddafi in Libya, with unarmed protesters facing live fire by both the security forces and loyalist militiamen and snipers.
But many Western officials have been reluctant to criticise Mr Assad too harshly, even though his regime has long been treated as a near pariah.
Hillary Clinton, the US secretary of state, initially sought to present Mr Assad as a reformist struggling against hardliners in his regime. Even Israel, which remains technically at war with Syria, has privately urged Washington to refrain from action that could destabilise Mr Assad for fear that his downfall could usher in a more hostile government.