The US Secretary of State has said Syrian President Bashar al-Assad has "lost legitimacy", amid diplomatic tension between the two countries.
Speaking after a crowd attacked the US embassy in Damascus, Hillary Clinton said Mr Assad was "not indispensable".
France blamed the regime after its embassy was similarly targeted.
The embassy attacks came after the US and French envoys visited the troubled city of Hama last week, drawing sharp criticism from Syrian media.
Pro-government demonstrators have been taking part in protests outside both embassies for the past two days.
On Monday, an embassy official told the BBC that the compound had been assaulted by a "mob", but that no-one had been hurt.
The residence of the ambassador, Robert Ford, was later briefly attacked, the state department said.
In Washington, Mrs Clinton demanded that the Syrians "meet their international responsibilities immediately to protect all diplomats and the property of all countries."
She added: "President Assad is not indispensable and we have absolutely nothing invested in him remaining in power.
"Our goal is to see that the will of the Syrian people for a democratic transformation occurs."
The BBC's Kim Ghattas in Washington said her statement was cleverly worded - it might convince more Syrians to give up on Mr Assad, while not requiring any action by Washington which can continue to say it is up to the Syrian people to chose their leaders.
Our correspondent adds that the US had been wary of a repeat of the Libya scenario, where after calling for Col Muammar Gaddafi to leave power, it has struggled to make that happen.
State department spokeswoman Victoria Nuland said a Syrian diplomat would be summoned over attack on the embassy, and compensation for the damage would be demanded.
Live shots
Also on Monday, pro-Assad demonstrators assaulted the French embassy, breaking windows and replacing the French tricolore with the Syrian national flag.
French ambassador Eric Chevallier said the incident had lasted more than three hours, and that the protesters had used a battering ram to try enter the building.
Three embassy staff were hurt in the incident, according to the French foreign ministry.
Ministry spokesman Bernard Valero said security officers had been forced to fire live warning shots "to prevent multiple intrusions into the compound".
"It is not with such illegal methods that the authorities in Damascus will turn the attention away from the fundamental problem, which is to stop the repression of the Syrian population," Mr Valero said.
Human rights groups say at least 1,400 civilians and 350 security force personnel have been killed since anti-government demonstrations across Syria began in mid-March.
Both Mr Chevallier and Mr Ford made separate visits to the northern city of Hama - a focus of anti-government unrest - last week, expressing support for the protesters.
The Syrian government denies targeting civilians, saying it is tackling armed groups.
The embassy incidents coincide with a government-organised dialogue conference in Damascus that many opposition leaders are boycotting.
The meeting is discussing possible political reforms, which the government hope will bring an end to the four-month-old uprising.
As the conference opened on Sunday, Vice-President Farouq al-Shara hinted at allowing political groups other than the ruling Baath Party to operate.
But Syrian opposition figure Michel Kilo dismissed the meeting saying: "I don't know anyone from the opposition to which I belong who is taking part in this dialogue."
