Syrian Christians have attended regular Sunday services for the first time since the dramatic overthrow of president Bashar al-Assad a week ago, in an early test of assurances by the new Islamist rulers that the rights of minorities will be protected.

As the jihadist group Hayat Tahrir al-Sham (HTS) swept to power last week, it sought to reassure Syria's minority groups that their way of life would not be at risk.

Before Assad fell, historical religious minority groups including Christians worshipped freely and some remain jittery at the prospect of an Islamist government.

Streets in the heavily Christian Damascus neighbourhood of Bab Touma filled with worshippers returning from church on Sunday morning but some struck a note of caution.

"We're scared, we're still scared," local resident Maha Barsa said after attending Mass at the local Greek Melkite Catholic church.

Barsa said she had barely left her home since HTS took over one week ago although she said that nothing had happened to warrant her concern, adding: "Things are ambiguous."

In the coastal city of Latakia, long an Assad stronghold, Lina Akhras, a parish council secretary at the St George Greek Orthodox Cathedral, said on Sunday that Christians had been "comfortable" under his rule in terms of freedom of belief but that they just wanted to live in peace and harmony.

"(Assad's fall) happened all of a sudden, we didn't know what to expect ... Thank God, we received a lot of assurances and we saw that members of the (HTS) committee reached out to our priest," she told Reuters.

"God willing, we will return to our previous lives and live in our beautiful Syria," Akhras added.

Syria is home to multiple ethnic and religious minorities including Christians, Armenians, Kurds and Shi'ite Muslims.

The Assad family itself belongs to the minority Alawite faith, an offshoot of Shi'ite Islam, in Sunni Muslim-majority Syria.

Tens of thousands of mostly Shi'ite Muslims have fled Syria for Lebanon in the last week out of fear of persecution by the country's new rulers, a senior Lebanese security official told Reuters last week.

The protection of Syria's minorities was a key concern on Saturday when top diplomats from Arab countries, Turkey, the United States and the European Union met in Jordan.

US Secretary of State Antony Blinken said they backed an inclusive and representative government that would respect minority rights and not offer "a base for terrorist groups".

Syrian students also returned to classrooms on Sunday after the new rulers ordered schools reopened in another potent sign of some normality.

The country's new de facto leader, Ahmad al-Sharaa - better known by his rebel nom de guerre Abu Mohammed al-Golani, faces a massive challenge to rebuild Syria after a civil war in which hundreds of thousands were killed.

Cities were bombed to ruins, the economy was gutted by international sanctions and millions of refugees still live in camps outside Syria.

Officials said most schools were opening around the country on Sunday, the first day of the working week.

However, some parents were not sending their children to class due to uncertainty over the situation.

As Syria starts trying to rebuild, its neighbours and other foreign powers are still working out a new stance on the country, a week after the collapse of Assad's government.

Sharaa leads HTS, a group formerly allied with al-Qaeda that is designated a terrorist organisation by the US, Russia, Turkey and Australia among other countries and is also under United Nations sanctions.

UN Syria envoy Geir Pedersen said on Sunday he hoped for a swift end to the sanctions to help facilitate economic recovery.

"We will hopefully see a quick end to sanctions so that we can see really rallying around building up Syria," Pedersen said as he arrived in Damascus to meet Syria's caretaker government.