Israeli Prime Minister Benjamin Netanyahu said Sunday he had ordered the Israeli military to "seize" a demilitarised buffer zone on the border with Syria after the overthrow of Bashar al-Assad in Damascus.

The Israeli premier said a 50-year-old "disengagement agreement" between the two countries had collapsed and "Syrian forces have abandoned their positions".

As a result, he said, "I directed the IDF (military) yesterday to seize the buffer zone and the commanding positions nearby. We will not allow any hostile force to establish itself on our border."

Iran's embassy in Syria was vandalised on Sunday, an AFP photographer said, after Islamist-led rebels declared the fall of Tehran ally Bashar al-Assad following a sweeping offensive that culminated in Damascus.

The AFP photographer saw ransacked offices, with shattered glass on the floor and broken furniture in the building in Damascus's upscale Mazzeh area, also home to other embassies and United Nations offices.

People loaded looted items onto trucks outside, the photographer said.

Syria's capital woke up Sunday to chanting, cheering and gunfire in celebration of the fall of President Bashar al-Assad, after rebels said they entered the city and toppled the longtime ruler.

"I can't believe I'm living this moment," tearful Damascus resident Amer Batha told AFP by phone from the capital's Ummayad Square, where witnesses said dozens of people had gathered to celebrate.

"We've been waiting a long time for this day," said Batha, as Islamist-led rebels and a war monitor declared the end of decades of Assad family rule amid 13 years of grinding civil war.

Syrians around the country on Sunday toppled and trampled on statues of President Bashar al-Assad's late father Hafez, who founded the brutal system of government that his son inherited.

In the capital Damascus, people cheered as they stood on a toppled statue of former president Hafez al-Assad, in a highly symbolic moment for a country ruled with an iron fist for five decades by his clan.

Syria's president Bashar al-Assad has fled Syria as Islamist-led rebels swept into Damascus Sunday, triggering celebrations across the country and beyond at the end of his oppressive rule.

Russian news agencies late Sunday said Assad and his family were in Moscow.

Crowds ransacked Assad's luxurious home after the rebels earlier Sunday declared he had fled, in a spectacular end to five decades of brutal Baath party rule.

In less than two months, Syria's Ahmed al-Sharaa has risen from rebel leader to interim president, after his Islamist group led a lightning offensive that toppled Bashar al-Assad.

Sharaa was appointed Wednesday to lead Syria for an unspecified transitional period, and has been tasked with forming an interim legislature after the dissolution of the Assad era parliament and the suspension of the 2012 constitution.

Syrian President Bashar al-Assad oversaw a merciless crackdown on a pro-democracy revolt that morphed into one of the bloodiest wars of the century.

On Sunday, as rebels entered the capital, a Syrian war monitor said he had left the country, in what could spell the end not just of his 24-year rule but the downfall of his clan's five-decade reign.

After facing down nationwide protests demanding his ouster and an armed rebellion that he all but crushed, Assad had -- until a lightning rebel offensive -- taken back control of much of Syria in the civil war that began in 2011.

Britain's leader Keir Starmer makes his first trip to the Gulf as prime minister from Sunday, seeking to attract investment from the region's oil-rich states, Downing Street announced.

Starmer will first visit the United Arab Emirates and then travel to Saudi Arabia, before stopping off in Cyprus on his way back to London on Tuesday in a bid "to build closer ties and drive long term UK growth".

In his office in central Berlin, Syrian human rights lawyer Anwar al-Bunni shook his head as he watched President Bashar al-Assad's government fighting for survival live on television.

He is one of more than a million Syrian refugees in Germany, many of whom have already taken to the streets in recent days to call for peace and freedom.

"Personally, I'm not surprised," said Bunni, 65, who served time in a Syrian jail before fleeing the country, arriving in Germany in 2014.

Panic gripped Damascus after fast-advancing rebels said on Saturday they had begun operations to surround Syria's capital, residents said, with many scrambling to stock up on vital supplies.

Protests spread like wildfire in neighbouring provinces, with anti-government demonstrators toppling statues of late president Hafez al-Assad in the Jaramana suburb of Damascus and in the southern city of Daraa.

Damascus resident Rania, who is in her eighth month of pregnancy, said she could not find desperately needed medicine anywhere as shops and pharmacies had closed early.