Clinton said China and India in particular could increase pressure because of their energy investments. She said the US did not want to call for Mr Assad to stand down without getting the backing of other countries.
Activists say the army killed at least 24 people on Thursday and new protests flared after dawn prayers on Friday. More than 1,700 people have died and tens of thousands of people have reportedly been arrested since the uprising against the the 41-year rule of President Bashar al-Assad's family began in March.