President Barack Obama said Syrian leader Bashar Al-Assad had lost legitimacy, as ties with Damascus nosedived after pro-regime protesters attacked the US and French embassies.

US rhetoric against Assad mounted after the attacks, also condemned by the UN Security Council and UN chief Ban Ki-moon, and a senior US official said Washington was mulling fresh sanctions against Assad and his inner circle.

Obama told CBS television Tuesday that Assad had "missed opportunity after opportunity to present a genuine reform agenda.

"More broadly, I think that increasingly you're seeing President Assad lose legitimacy in the eyes of his people," Obama said.

Washington had made it clear "that what we've seen on the part of the Syrian regime has been an unacceptable degree of brutality directed at its people," the US president said.

Mobs attacked 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.

Obama also scolded Syria, saying Washington had "sent a clear message that nobody can be messing with our embassy and that we will take whatever actions necessary in order to protect our embassy."

Assistant Secretary of State for Human Rights Michael Posner told US lawmakers at a hearing on Capitol Hill that there could be further sanctions than those signed by Obama in an executive order in May.

Those sanctions allow Washington to freeze any assets owned in the United States by Assad and his top aides and ban any individuals or US companies from dealing with them.

"We've done quite a bit already and we're exploring other sanctions," Posner said, adding that the situation in Syria "remains grim," with "numerous reports of attacks on civilians, including children."

Syria meanwhile 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."

In Damascus, a regime-backed "national dialogue" on reforms wrapped up a three-day meeting with calls for the release of all political detainees. It was attended by about 200 delegates but boycotted by the opposition.

Independent MPs and members of Assad's Baath party, which has been in power since 1963, took part in the talks.

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 that the council take a stance.

"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," German Foreign Minister Guido Westerwelle 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 "extremely violent" and warning Assad's regime was losing its grip.

On Monday, three staff were injured in the attack on the French embassy, forcing guards to fire three warning shots.

As Syrian security forces looked on, Assad supporters smashed their way into the embassy compound with a battering ram, broke windows and destroyed the ambassador's car, according to a foreign ministry spokesman in Paris.

At the US embassy, several demonstrators 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. No one was injured.