The officials spoke on condition of anonymity in line with government regulations.
Despite mounting international condemnation, Assad's regime has largely held together. On Saturday, however, France announced the defection of Brig. Gen. Manaf Tlass, an Assad confidant and son of a former defense minister who helped ease Assad into power.
Tlass is the highest ranking official to abandon the regime so far, and Western powers and anti-regime activists hoped his departure would encourage others to leave, too.
News of the defection largely overshadowed an international conference in Paris on Saturday attended by the U.S., its European and Arab partners and members of Syria's fractured opposition.
The so-called "Friends of Syria" said they would provide means for the opposition in Syria to better communicate among themselves and with the outside world and increase humanitarian aid.
They also called on the U.N. Security Council to adopt a resolution that would force the regime to comply with the two peace plans that have been largely ignored by both sides in the conflict.
Syrian allies Russia and China would likely veto any resolution seen as too critical of the Syrian government, as they have in the past.
About 100 demonstrators marched against Assad's regime in Paris on Saturday. Many were disappointed that the Paris conference had not led to more specific actions against the regime.
"Meeting just to talk is useless," said protester Hende Khattav, a Syrian who has lived in Paris for 37 years. "We have to do something. There has to be a useful action to make this massacre of the Syrian people stop."