Russia's Foreign Ministry said earlier that Assad had left Syria and given orders for a peaceful transfer of power, after rebel fighters raced into Damascus unopposed on Sunday, ending nearly six decades of his family's iron-fisted rule.
"Syrian President Assad of Syria and members of his family have arrived in Moscow. Russia has granted them asylum on humanitarian grounds," the privately-owned Interfax news agency and state media quoted the unnamed Kremlin source as saying.
Interfax cited the same Kremlin source as saying Russia favoured a political solution to the crisis in Syria, where Moscow supported Assad during the long civil war.
The source said negotiations should be resumed under the auspices of the United Nations.
Mikhail Ulyanov, Russia's ambassador to international organisations in Vienna, said on his Telegram messaging channel: "Breaking news! Bashar al-Assad and his family in Moscow. Russia does not betray friends in difficult situations."
Syrian opposition leaders had agreed to guarantee the safety of Russian military bases and diplomatic institutions in Syria, the source told news agencies. But some Russian war bloggers said the situation around the bases was extremely tense and the source did not say how long the security guarantee lasted.
Moscow, a staunch backer of Assad whom it intervened to help in 2015 in its biggest Middle East foray since the Soviet collapse, is scrambling to salvage its position. Its geopolitical clout in the wider region and two strategically-important military bases in Syria are on the line.
A deal to secure Russia's Hmeimim air base in Syria's Latakia province and its naval facility at Tartous on the coast would come as a relief to Moscow.
The Tartous facility is Russia's only Mediterranean repair and replenishment hub, and Moscow has used Syria as a staging post to fly its military contractors in and out of Africa.
Losing Tartous would be a serious blow to Russia's ability to project power in the Middle East, the Mediterranean and Africa, say Western military analysts.
MILITARY PRESENCE IN DOUBT
Influential Russian war blogger "Rybar", who is close to the Russian Defence Ministry and has over 1.3 million followers on his Telegram channel, said the situation around the bases was a serious cause for concern whatever Moscow's official line.
"Russia's military presence in the Middle East region hangs by a thread," Rybar said.
"What anyone decided in high offices is absolutely irrelevant on the ground," he added, suggesting Russian forces at the bases had not taken the initiative to defend their positions in the absence of orders from Moscow.
Russian warships had left Tartous and taken up position off the coast for security reasons, the Hmeimim airbase had effectively been cut off after rebels took control of a nearby town, Kurdish forces had started to block Russian facilities beyond the Euphrates, and Russian positions at an oil facility in Homs had been blocked, Rybar said.
Reuters could not independently confirm Rybar's assertions.
Earlier on Sunday, the Russian Foreign Ministry said in a statement that the two military facilities had been put on a state of high alert, but played down any immediate risk.
"There is currently no serious threat to their security," the ministry said as it announced Assad's departure from office and from Syria.
"As a result of negotiations between B. Assad and a number of participants in the armed conflict on the territory of the Syrian Arab Republic, he decided to resign from the presidency and left the country, giving instructions for a peaceful transfer of power," it added, saying Russia did not participate in those negotiations.
The Foreign Ministry said Moscow was alarmed by events in Syria.
"We urge all parties involved to refrain from the use of violence and to resolve all issues of governance through political means," its statement said.
"In that regard, the Russian Federation is in contact with all groups of the Syrian opposition."
