Angry mobs stormed the American and French embassies in Syria on Monday, after the two Western envoys visited the city of Hama, a flashpoint for protests against President Bashar al-Assad's regime.

The foreign ministry in Paris said three French staff were wounded in the embassy attack, while a US official said "no staff were injured."

Guards at the French embassy had to fire three warning shots, the foreign ministry said.

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

An AFP photographer at the scene said several windows in the French embassy were broken and Syrian flags were raised.

"A car belonging to an embassy staffer was damaged and a picture of the Syrian president was stuck on it," he said.

The US embassy official told AFP: "Today there was an attack by a mob on the US embassy," adding the crowd caused some damage to the mission.

Monday's embassy attacks come four days after US Ambassador Robert Ford and his French counterpart Eric Chevallier visited the central city of Hama, 210 kilometres (130 miles) north of Damascus, sparking outrage in the capital.

Their visits took place amid fears of a bloody crackdown after Friday prayers the next day by Assad's forces, with tanks encircling the city.

The US embassy official said "no staff were injured" on Monday and were never in "imminent danger," although the "Syrian government was slow to respond with extra security measures that were needed."

"The Syrian government has assured us that it will provide the protection required under the Vienna Convention and we expect it to do so."

He added that a Syrian television channel had "encouraged this violent demonstration," which followed protests at the embassy on Friday and Saturday calling for the ambassador's resignation.

On Sunday, a senior US official had accused Damascus of orchestrating the protests over Ford's trip to Hama, which the authorities slammed as a "flagrant interference" in Syria's "domestic affairs."

In Washington on Monday, a State Department spokesperson said: "We strongly condemn the Syrian government's refusal to protect our embassy, and demand compensation for damages.

"We call on the Syrian government to fulfill its obligations to its own citizens as well."

Ambassador Ford, in a US embassy Facebook post dated Sunday morning and referring to a protest outside the embassy on Saturday, said demonstrators "resorted to violence, unlike the people in Hama, who have stayed peaceful."

"And how ironic that the Syrian government lets an anti-US demonstration proceed freely while their security thugs beat down olive branch-carrying peaceful protesters elsewhere," he wrote.

France on Sunday summoned Syria's envoy to Paris Lamia Shakkour over damage to the French embassy and a consulate in Aleppo on Saturday after Chevallier's trip to Hama.

Foreign Minister Alain Juppe's cabinet chief called her to the ministry to receive a "vigorous protest", ministry spokesman Bernard Valero said in a statement.

Tensions have been escalating for months between Damascus and Washington over the Syrian government's fierce response to pro-democracy protests that erupted in mid-March.

Human rights groups say that since the protests broke out, the security forces have killed more than 1,300 civilians and made at least 12,000 arrests.

Protests were also staged overnight in several towns against Sunday's opening of a "national dialogue" hailed by the regime but boycotted by the opposition, rights activists said.

Some 5,000 people demonstrated in Deir Ezzor in the east, the London-based Syrian Observatory for Human Rights reported, adding there were also protests in three districts of Damascus.

The army was also reported to be conducting a search and sweep operation in the Jebel al-Zawiya area of Idlib province in the northwest.

"Soldiers supported by tanks carried out searches in the villages of Kafarhaya, Sarjan and Al-Rami, and arrests were made in Kfar Nubol," the Observatory said.

People were also detained in Hama and in the coastal city of Banias, where the rights group reported five arrests of people "for filming demonstrations."

Shooting was also heard at around dawn in the central city of Homs.

A meeting of the "national dialogue" in the capital was due to take place later on Monday.

Sunday's inaugural session saw some 200 delegates take part, including independent MPs and members of the Baath party, in power since 1963.

Opposition figures boycotted the gathering in protest at the government's ongoing deadly crackdown on the anti-regime protests.

Meanwhile, the number of Syrian refugees in Turkey fell to about 8,500 as hundreds decided to return home over the weekend, Turkish officials in Ankara said on Monday.

The number of refugees fleeing the government crackdown and entering Turkey peaked at 11,739 at the end of June, when Syrian troops stormed border villages where many displaced people had massed.