The European Union has threatened more sanctions against Syria if the government crackdown on dissent continues.
EU leaders warned Damascus Sunday they "will impose further and more comprehensive measures against the regime" as long as the government continues to repress the civilian population.
The European bloc already has an embargo on crude oil imports from Syria, has banned investment in the country's oil sector, and has forbidden EU-based operators from participating in joint ventures with Syrian companies or providing credits and loans.
The effect of these measures has been blunted by Russia and China's block of a U.N. Security Council resolution that could have led to broader action.
The EU Sunday also issued a fresh call for Mr. Assad to "step aside" and called the creation of the Syrian National Council "a positive step forward." It said the Syrian people must be able to define their future "without fear of repression."
U.S. Senator John McCain went even further Sunday, saying military action to protect Syrian civilians may be possible now that NATO's air campaign in Libya is ending.
McCain said Mr. Assad's government "should not consider that it can get away with mass murder." He noted that Libya's ousted leader Moammar Gadhafi made that mistake and it "cost him everything."
The influential Republican senator, speaking Sunday in Jordan, also charged that "dark forces in the region, especially in Iran, are working to hijack the promise of...the Arab Spring." McCain said these concerns "are real and legitimate and merit our vigilance."
Most Syrian opposition groups have said they oppose military intervention, and NATO allies have shown little inclination for mounting such a campaign in another Arab state. There also is real concern that Mr. Assad's ouster would spread chaos around the region.
Earlier Sunday, the Syrian leader replaced governors in two provinces that have had months of protests against his 11-year rule. Syria's state news agency said the president appointed Hussein Makhlouf to run the rural areas surrounding Damascus, and Yasser al-Shoufi to govern northern Idlib province, near Turkey.
Mr. Assad has fired several other provincial governors since nationwide protests erupted in March. The United Nations says his ongoing crackdown has killed more than 3,000 people. The government says terrorist gangs have killed hundreds of security personnel in the unrest.
In the latest violence, rights groups said government forces shot and killed two people in the central province of Hama early Sunday. Activists said security forces also broke up an opposition protest strike in southern Daraa province that began Thursday.
There was no independent confirmation of the strike or the latest violence. Syria has barred most international media from operating in the country.
Some information for this report was provided by AP, AFP and Reuters.