Secretary of State Hillary Clinton hinted the United States might be making some headway in persuading European nations, China or India to curtail their energy ties with Syria, saying "stay tuned" when asked what progress Washington had made.
Clinton has said the best way pressure Syria to stop crushing protests against the 41-year Assad regime was by sanctioning its oil and gas sector but that this was largely up to other nations because there is little U.S. involvement.
Syrian forces shot dead 13 protesters on Friday, activists said, as tens of thousands demanded Assad's overthrow chanting "we will kneel only to God."
Defiant protest marches unfolded across the country including in the cities of Hama and Deir al-Zor, both of which have been stormed in tank offensives launched by Assad during the holy month of Ramadan.
Speaking at a news conference with Norwegian Foreign Minister Jonas Gahr Stoere, Clinton stopped short of explicitly calling for Assad's departure. On Thursday, she suggested the United States wanted other nations to join in such a call.
"We urge those countries still buying Syrian oil and gas, those countries still sending Assad weapons, those countries whose political and economic support give him comfort in his brutality, to get on the right side of history," she said.
U.S. officials who spoke on condition of anonymity said it was the first time Washington had explicitly called for a boycott of Syrian oil since anti-Assad protests erupted in March after popular upheavals toppled authoritarian leaders in Egypt and Tunisia.
Syria's crude oil production of 380,000 barrels a day generates most of the state's hard currency. According to the U.S. Energy Information Administration, Syrian crude exports go mostly to European nations such as Germany, Italy and France.
"President Assad has lost the legitimacy to lead and it is clear that Syria would be better off without him," she added at the news conference, echoing previous comments by the Obama administration.
Syrian forces fired live ammunition at protesters coming out of a main mosque after Friday prayers in the besieged city of Deir al-Zor, witnesses said, as demonstrations against the Assad family's 41-year rule resumed elsewhere in the country.
Activists say more than 1,700 civilians in all have been killed in the military crackdown on protests against Assad which broke out in March. Syria blames the violence on armed groups, who it says have killed 500 soldiers and police.