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Syria's new prime minister said the alliance that ousted president Bashar al-Assad will "guarantee" the rights of all religious groups and called on the millions who fled the war to return home.

Assad fled Syria after a lightning offensive spearheaded by the Hayat Tahrir al-Sham (HTS) group and its allies, which brought to a spectacular end five decades of brutal rule by his clan.

Syrians across the country and around the world erupted in celebration, after enduring a stifling five decades that saw anyone suspected of dissent thrown into jail or killed.

With Assad's overthrow plunging Syria into the unknown, its new rulers have sought to assure members of the country's religious minorities that they will not repress them.

HTS has been proscribed as a terrorist organisation by many Western governments, though the group has sought to moderate its rhetoric.

"Precisely because we are Islamic, we will guarantee the rights of all people and all sects in Syria," said Mohammad al-Bashir, whom the rebels appointed as the transitional head of government.

Asked whether Syria's new constitution would be Islamic, he told Italian daily Corriere della Sera that "we will clarify all these details during the constituent process".

Bashir, whose appointment was announced Tuesday, is tasked with heading the multi-ethnic, multi-sectarian country until 1 March.

After decades of iron-fisted rule by the Assads -- adherents of the minority Alawite offshoot of Shiite Islam -- Syrians now face the enormous challenge of charting a new course as they emerge from nearly 14 years of war.

Roaming the opulent Damascus home of Assad, Abu Omar felt a sense of giddy defiance being in the residence of the man he said had long oppressed him.

"I am taking pictures, because I am so happy to be here in the middle of his house," said the 44-year-old.

"I came for revenge. They oppressed us in incredible ways," he added.

'Free country' 

The war has killed more than 500,000 people and forced half the population to flee their homes, with six million of them seeking refuge abroad.

In his interview with Corriere della Sera, which was published on Wednesday, Bashir called on Syrians abroad to return to their homeland.

"Mine is an appeal to all Syrians abroad: Syria is now a free country that has earned its pride and dignity. Come back," he said.

"We must rebuild, be reborn and we need everyone's help."

He also said that Syria's new rulers would be willing to work with anyone so long as they did not defend Assad.

"We have no problem with anyone, state, party or sect, who kept their distance from the bloodthirsty Assad regime," he said.

Assad was propped up by Russia, where he reportedly fled, as well as Iran and Lebanon's Hezbollah militant group.

On Wednesday, the Kremlin said it wanted to see rapid stabilisation in Syria, as it criticised Israel over hundreds of air strikes it conducted on its neighbour over the past two days.

"We would like to see the situation in the country stabilised somehow as soon as possible," Kremlin spokesman Dmitry Peskov told reporters.

Russia was continuing to discuss the fate of its military infrastructure in the country with Syria's new leadership, he added.

Iran, meanwhile, upheld its view that Assad's overthrow was a "product of a joint US-Israeli plot".

Its supreme leader, Ayatollah Ali Khamenei, said Wednesday that the ouster of Assad would not weaken its anti-Israel "resistance".

'Test him' 

While Assad had faced down protests and an armed rebellion for more than a decade, it was a lightning offensive launched on 27 November that ended up forcing him out of power.

The rebels launched their offensive from northwest Syria on the very same day that a ceasefire took effect between Israel and Hezbollah in neighbouring Lebanon.

That war, where Israel killed thousands in Lebanon, also saw Israel inflict staggering losses among Hezbollah's ranks.

Qatar on Wednesday said it would reopen its embassy in Damascus "soon", while US Secretary of State Antony Blinken is expected in Turkey on Friday to discuss developments in Syria.

Robert Ford, the last US ambassador to Syria, helped spearhead the terrorist designation of HTS in 2012, but said that in the past few years the group has not attacked US or Western targets and has instead fought Al-Qaeda and Islamic State group forces.

Ford also pointed with hope to post-victory statements by rebel chief Abu Mohammed al-Jolani, including welcoming international monitoring of any chemical weapons that are discovered.

"Can you imagine Osama bin Laden saying that?" said Ford, now a senior fellow at the Middle East Institute.

"I'm not saying 'trust Jolani.' He's obviously authoritarian. He's obviously an Islamist who doesn't believe that Christians have an equal right to power as Muslims. But I sure as hell want to test him on some of these things," he added.