Syria accused US Secretary of State Hillary Clinton of "incitement" after she maintained Assad had lost legitimacy and the right to remain in power.
"Syria vigorously condemns the remarks of the US secretary of state that amount to further proof of the flagrant interference of the United States in the internal affairs of Syria," said its foreign ministry.
"These remarks are an act of incitement aimed at continuing the internal crisis and for objectives which do not serve the interests of the Syrian people or their legitimate ambitions."
Clinton's comments came after mobs besieged the US and French embassies on Monday after the ambassadors of the two Western countries last week travelled to the flashpoint protest city of Hama, north of the capital.
"President Assad is not indispensable and we have absolutely nothing invested in him... remaining in power," she said. "From our perspective, he has lost legitimacy."
The White House on Tuesday slammed Syria for allowing "thugs" to overrun the US embassy, saying it is "not acceptable" that the government failed to safeguard US lives and property there.
"We've made that clear to the Syrian government. It's their responsibility... to provide security for and maintain security for foreign embassies, in this case, the US embassy," said spokesman Jay Carney.
In Syria, about 200 delegates on Tuesday closed talks on reform boycotted by the opposition pledging to work with parties inside and outside the country to prepare a "national dialogue conference as soon as possible."
"Dialogue is the only way to halt the crisis," they said in a final statement, adding the opposition was an "integral part" of Syria's political life.
Independent MPs and members of Assad's Baath party, which has been in power since 1963, took part in the talks, but opposition figures boycotted in protest over the deadly crackdown.
Activists said Tuesday on their Facebook page they opposed any Libya-style military intervention and called for greater economic and political pressure on Damascus.
They also called for Assad to be referred to the International Criminal Court, on their Syrian Revolution 2011 page which has been an engine of the popular revolt.
Activists say 1,300 civilians have been killed and 12,000 arrested since mid-March.
Germany said Tuesday it would push for a UN Security Council resolution condemning Syria over the crackdown, after France renewed its demand the council take a stance.
"We should not forget: hundreds of thousands of normal people, young people demonstrating for their own freedom," said German Foreign Minister Guido Westerwelle.
"What has happened in the last days and hours shows us that the common language of the international community is necessary, is decisive, is crucial," he told journalists in New York.
Earlier, French Prime Minister Francois Fillon said: "France and other European countries have submitted a proposed resolution to the UN Security Council, which has been blocked by Russia and China.
"This is no longer acceptable," he said, branding the attack on his government's Damascus embassy, in which three French personnel were wounded, "extremely violent" and warning Assad's regime was losing its grip.
On Monday, three staff were injured in the attack on the French embassy in Damascus, forcing guards to fire three warning shots.
As Syrian security forces looked on, Assad supporters smashed their way into the French embassy compound with a battering ram, broke windows and destroyed the ambassador's car, according to a foreign ministry spokesman in Paris.
Last week, the French and US ambassadors to Syria made high-profile visits to the restive city of Hama.
Syria's state news agency SANA said hundreds of people on Monday also held a sit-in in front of the French consulate in Aleppo, accusing Paris of "mobilising the international community" against Damascus.
At the US embassy, several demonstrators on Monday scaled the complex's high outer wall and others draped a large Syrian flag over the main entrance.
The chancery was not breached but some of the crowd of about 300 climbed up on the roof and reached ambassador Robert Ford's residence before being chased away by US marines. Nobody was injured.
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