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Syrian Prime Minister Mohammed al-Jalali said Sunday he was ready to "cooperate" with any leadership chosen by the people, after rebels said "tyrant" President Bashar al-Assad had fled the country.

The leader of the Islamist Syrian rebel group Hayat Tahrir al-Sham, Abu Mohammed al-Jolani, ordered forces not to approach official institutions in Damascus, saying they would remain under the prime minister until they were "officially" handed over.

Hayat Tahrir al-Sham (HTS) and allied factions have pressed a lightning offensive since November 27, sweeping swathes of the country from regime control, including major cities Aleppo, Hama and Homs.

Provinces in the country's south and east have also fallen from the hands of the regime after local fighters seized control and Assad's forces withdrew.

The rebels said early Sunday that "the tyrant Bashar al-Assad has fled" and declared "the city of Damascus free".

"After 50 years of oppression under Baath rule, and 13 years of crimes and tyranny and (forced) displacement... we announce today the end of this dark period and the start of a new era for Syria," the rebels said on Telegram.

In a speech broadcast on his Facebook account, premier Jalali said "this country can be a normal country that builds good relations with its neighbours and the world".

"But this issue is up to any leadership chosen by the Syrian people. We are ready to cooperate with it (that leadership) and offer all possible facilities," he added.

Jalali said he was "ready for any handover procedures".

Rebel leader Jolani said in a statement on Telegram: "To all military forces in the city of Damascus, it is strictly forbidden to approach public institutions, which will remain under the supervision of the former prime minister until they are officially handed over."

"It is forbidden to shoot into the air," added Jolani, who has started using his real name Ahmed al-Sharaa instead of his nom de guerre.

Rami Abdel Rahman, head of the Syrian Observatory for Human Rights war monitor, said "Assad left Syria via Damascus international airport before the army security forces left" the facility.