World leaders are reacting to the fall of Syrian President Bashar al-Assad’s government in a rapid rebel offensive that took the world by surprise.

Islamist rebels seized control of Damascus on Sunday (local time), forcing Assad to flee, ending his family’s decades of rule after more than 13 years of civil war in a seismic moment for the Middle East.

Russian news agencies, citing a Kremlin source, are reporting Assad and his family have arrived in Russia and have been granted asylum there.

The news has sparked celebrations on streets across the Middle East and Europe.

The rebels also dealt a major blow to the influence of Russia and Iran in Syria in the heart of the region. The allies propped up Assad during critical periods in the conflict.

Rebels said they entered the Syrian capital on Sunday with no sign of army deployments.

Thousands of people in cars and on foot congregated at a main square waving and chanting “Freedom” from a half century of Assad family rule, witnesses said.

There are celebrations in Syrian communities worldwide, including in Tripoli, northern Lebanon. Photo: AAP

People were seen walking inside the Al-Rawda Presidential Palace, with some leaving carrying furniture from inside. The rebels said prisoners had been freed from a large jail on the outskirts of Damascus where the Syrian government detained thousands.

“We celebrate with the Syrian people the news of freeing our prisoners and releasing their chains,” the rebels said.

Iran’s embassy was also stormed by Syrian rebels, Iran’s English-language Press TV reported.

Hezbollah, which provided crucial support to Assad for years, withdrew all of its forces from Syria on Saturday as rebel factions approached the capital Damascus, two Lebanese security sources told Reuters on Sunday.

One of the sources said the supervising forces that Hezbollah had deployed to Syria late on Thursday had been sent to oversee the pullback.

Syria’s army command notified officers on Sunday that Assad’s rule had ended, a Syrian officer who was informed of the move told Reuters.

A bust of the former Syrian President Hafez Assad was toppled in Damascus. Photo: AAP

Assad, who has not spoken in public since the sudden rebel advance a week ago, flew out of Damascus for an unknown destination earlier on Sunday, two senior army officers told Reuters.

His whereabouts now – and those of his wife Asma and their two children – remain unconfirmed, despite the reports they are in Moscow.

The Russian Foreign Ministry said Assad had left office and departed the country after giving orders for a peaceful handover of power.

The Syrian rebel coalition said it was continuing work to complete the transfer of power to a transitional governing body with full executive powers.

“The great Syrian revolution has moved from the stage of struggle to overthrow the Assad regime to the struggle to build a Syria together that befits the sacrifices of its people,” it said.

As Syrians expressed joy, Prime Minister Mohammad Ghazi al-Jalali called for free elections.

But that would require a smooth transition in a country with complex competing interests, from Islamists to groups with links to the US, Russia and Turkey.

Middle East shift

The collapse of Assad’s rule followed a shift in the balance of power in the Middle East after many leaders of Lebanon’s Iranian-backed Hezbollah group, a lynchpin of Assad’s battlefield force, were killed by Israel over the past two months.

The pace of events has stunned Arab capitals and raised fears of a wave of regional instability.

It marks a turning point for Syria, shattered by years of war that has turned cities to rubble, killed hundreds of thousands of people, and forced millions abroad as refugees.

Stabilising western areas of Syria captured in the rebels’ advance will be key.

Western governments, which have shunned the Assad-led state for years, must decide how to deal with a new administration in which a globally designated terrorist group – Hayat Tahrir al-Sham (HTS) – looks set to have influence.

The US will continue to maintain its presence in eastern Syria and will take steps to prevent a resurgence of the Islamic State, Deputy Assistant Secretary of Defence for the Middle East Daniel Shapiro told the Manama Dialogue security conference in Bahrain’s capital on Sunday.

“The real question is how orderly will this transition be, and it seems quite clear that Golani is very eager for it to be an orderly one,” said Joshua Landis, a Syria expert and Director of the Center for Middle East Studies at the University of Oklahoma.

Golani will not want a repeat of the chaos that swept Iraq after US-led forces toppled Saddam Hussein in 2003.

-with AAP