Warships led by Russia's sole aircraft carrier, Admiral Kuznetsov, will be the first to leave the conflict area, the chief of the Russian Armed Forces General Staff, Gen. Valery Gerasimov, is quoted as saying.
It is not clear if the Kuznetsov's warplanes will leave with it or if any will stay behind in Latakia, Syria.
The reported initial withdrawal of forces come as a nationwide ceasefire -- negotiated between Russia, Turkey and the Syrian government
as well as Iran and Syrian rebel groups late last year -- largely holds across the country, according to the United Nations.
Russia's air strikes since 2015 in support of the forces of Syrian President Bashar al-Assad have been crucial in helping them to gain the upper hand in the long-running conflict and pushing rebel fighters from the key city of Aleppo in December.
The decision to cut Russia's military presence in Syria was made by Putin at the recommendation of his Defense Minister Sergei Shoigu on December 29, according to Russia's state-run agency Sputnik.
"In accordance with the decision of Supreme Commander-in-Chief of the Russian Armed Forces Vladimir Putin, the Defense Ministry is beginning to reduce the Armed Forces grouping in Syria," Gerasimov reportedly said.
The warships led by the Kuznetsov will leave the Mediterranean on Friday headed for Severomorsk, in Russia's northern Murmansk region, Gerasimov said.
The commander of the Russian military force in Syria, Col. Gen. Andrei Kartapolov, was quoted by Sputnik Friday as saying that war planes operating from the aircraft carrier group had carried out 420 sorties in two months, destroying "1,252 terrorist targets" in Syria. They began operations off Syria's coast on November 8, Sputnik said.
If the ceasefire holds, peace negotiations are slated to take place in late January in Astana, Kazakhstan.
But rebel groups have complained of "Syrian regime violations" since the ceasefire came into force December 30 and warned that they could boycott the talks
if they continue.
The Free Syrian Army and other armed groups say the regime is continuing its siege of rebel-held areas outside Damascus -- and claim government forces have launched an assault on Wadi Barada, which supplies the capital with much of its water.
The opposition fears the regime is using the truce
to regroup and selectively pick off rebel-held areas it wants to regain. But the regime says it's going after "terrorists" who were deliberately excluded from the agreement.
UN: 'It is not over'
The UN special envoy for Syria, Staffan de Mistura, said Thursday that he welcomed the UN Security Council's unanimous support of a resolution backing the ceasefire plan brokered by Russia and Turkey.
"There are incidents, we know about them, we are informed, and we are trying and hoping that the two guarantors, and we trust they will, succeed in overcoming them so that they reach the point in which the cessation of hostilities will be recognized and working this time," he said.
The United Nations hopes that positive talks in Kazakhstan will lead in to talks in Geneva, Switzerland, in February, he said.
Jan Egeland, the UN senior adviser on Syria, speaking at the same briefing, said there was "a lot of fighting" in rural Damascus, as well as Homs and Hama, which had meant five out of 21 locations for planned aid convoys had been denied.
"So it is not over, even though the cessation of hostilities is largely holding in large parts of the country, there are tremendous dramas for the civilian population still, and we are denied access still in too many places," he said.
US Secretary of State John Kerry said Thursday that he had been in contact with his Russian and Turkish counterparts and others, "talking about how we would build conceivably on what happens in Astana, if it can happen, in order to get to Geneva and get to the real negotiations that the international community supports."