Syrian President Bashar Assad, left, and Russian President Vladimir Putin shake hands during their meeting in Moscow, July 24. AP-Yonhap

The Kremlin declined on Monday to confirm reports that toppled Syrian president Bashar al-Assad had fled to Moscow, adding that it was "surprised" by the rebel takeover.

"As for Mr Assad's whereabouts, I've got nothing to tell you," Kremlin spokesman Dmitry Peskov told journalists.

A Kremlin source told Russian news agencies on Sunday that Assad and his family were in Moscow, hours after he fled the country as Islamist-led rebels entered Damascus.

Assad's son has been studying in the Russian capital.

Peskov said on Monday that if Russia granted asylum to Assad and his family, this would be a decision taken by Russian President Vladimir Putin.

"Of course such decisions cannot be taken without the head of state, and it's his decision," Peskov said.

He said there was no meeting with Assad on Putin's agenda.

Russia has given shelter to several ousted leaders, including former Ukrainian president Viktor Yanukovych.

In brief comments on the dramatic events in Syria over the last few days, Peskov admitted the Kremlin was taken by surprise.

"What happened has surprised the whole world and, in this case, we are no exception," he said.

Russia has strategically important army and naval bases in Syria, where it launched a military intervention on the side of Assad in 2015.

"Now there will be a very complex period due to instability," Peskov said.

Asked what would happen to Russia's bases, he said: "It is too early to say. This is a subject for discussion with whoever is going to be in power in Syria."

The Kremlin spokesman said that the security of the bases was "very important."

"We are doing everything that is possible and necessary to get in touch with those who can provide security. And our military are also taking precautionary measures," it said.

The Kremlin source quoted by Russian news agencies on Sunday had said the rebels who ousted Assad "guaranteed the security of Russian army bases and diplomatic institutions on Syria's territory."

Syria's embassy in Moscow raised the opposition flag at the building on Monday, with a spokesman saying the facility was operating normally.

Peskov said Russia was "in dialogue" with Turkey, which supported rebel forces in Syria, saying: "Here it's important to maintain dialogue with all countries. We firmly intend to do this and analyse the situation." (AFP)