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.

"I'm very scared, for me and for my unborn daughter," she told AFP.

"I've been trying to buy medicine since this morning but I cannot find what I need."

Rania said she had to come home empty-handed after her husband demanded that she return.

"The situation was not like this when I left my house this morning... suddenly everyone was scared," she said.

Rebels said earlier onSaturday they had begun operations to encircle the government-held capital after seizing nearby towns.

Syria's defence ministry denied the army had fled positions near the city.

Residents spoke to AFP of a state of panic as traffic jams clogged central Damascus and people sought supplies and queued to withdraw money from ATM machines.

Three residents, who requested anonymity for security reasons, said they struggled to find food or medicines as stores had shut.

Rumours that President Bashar al-Assad had fled the country added to the anxiety, although his office denied the reports and said he was still in Damascus.

Assad last appeared in public on Sunday during an official visit by Iran's Foreign Minister Abbas Araghchi.

'Syria is ours'

Security forces and the army were deployed in the Mazzeh neighbourhood, which is home to embassies, United Nations offices and security headquarters.

Interior Minister Mohammed al-Rahmoun told state television that security forces had imposed an impenetrable cordon around the city, while he toured the capital in a bid to "reassure" citizens.

The mood was starkly different a few kilometres (miles) away, in the southern Damascus suburb of Jaramana where anti-government protesters toppled a statue of Assad's father, witnesses told AFP.

Statues were also toppled in Hama, seized by rebels within days of snatching the second city Aleppo -- in scenes reminiscent of the mass anti-government protests that swept the country in 2011.

In Jaramana, which is home to mostly Druze, Christians and families displaced by more than a decade of civil war, video footage verified by AFP showed young men chanting: "Syria is ours, it doesn't belong to the Assad family."

One witness said by phone that he saw "dozens of protesters" tear down the statue of Assad's father in a main square in Jaramana that bears the former president's name.

Another witness who passed through the square later said the statue had been smashed.

Damascus resident Mohammed, 35, told AFP he felt "a mix of shock, fear and worry about the future".

"Nothing compares to what we're going through today. But I think we're witnessing days that will go down in history," he added.