(CNN) Russian President Vladimir Putin announced Monday that he has ordered Russian forces to begin withdrawing from Syria, saying they have achieved their goals in the country.

The pullback will begin Tuesday, the state-run Sputnik news agency reported.

"I think that the task that was assigned to the Ministry of Defense and the armed forces as a whole has achieved its goal, and so I order the defense minister to start tomorrow withdrawing the main part of our military factions from the Syrian Arab Republic," Putin said.

Russia began airstrikes in September in support of the Syrian government in a civil war that is now nearly five years old.

Airstrikes have caused 'substantial damage'

Putin discussed the decision with Syrian President Bashar al-Assad in a telephone call.

"The two leaders noted that the operations conducted by Russia's Aerospace Forces have brought about a real turnabout in the fight against the terrorists in Syria, throwing their infrastructure into disarray and causing them substantial damage," the Kremlin said.

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"In this context, Mr. Putin said that Russia's Armed Forces have fulfilled their main mission in Syria and a timetable for the withdrawal of the Aerospace Forces' main air grouping has been agreed. Russia will maintain an aviation support centre in Syria in order to monitor compliance with the ceasefire."

Assad "noted the professionalism, courage and heroism of the Russian service personnel who took part in the military operations, and expressed his profound gratitude to Russia for providing such substantial help in fighting terrorism and providing humanitarian assistance to the civilian population," the Kremlin said.

Putin also had a conversation about Syria with U.S. President Barack on Monday.

"They discussed President Putin's announcement today of a partial withdrawal of Russian forces from Syria and next steps required to fully implement the cessation of hostilities with the goal of advancing the political negotiations on resolution of the conflict. President Obama welcomed the much-needed reduction in violence since the beginning of the cessation, but stressed that continuing offensive actions by Syrian regime forces risk undermining both the Cessation of Hostilities and the UN-led political process," according to a statement from the White House.

Peace talks resume in Geneva

A partial truce involving Syria's government and numerous rebel groups -- but not terrorist organizations like ISIS and al Nusra Front, which have been responsible for some of the worst carnage -- took effect late last month.

Military analysts said the Russian intervention helped push back rebel and ISIS forces and bolster the position of Assad, whose government, for a time, appeared to be teetering on the edge.

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"Nobody knows what is in Putin's mind, but the point is he has no right to be in be our country in the first place. Just go," said a spokesman for the main Syrian opposition group, the High Negotiations Committee.

The announcement of the withdrawal comes the same day as Syrian peace talks resumed in Geneva , Switzerland, and some see it as evidence that Putin is sending a message to Syrian and other forces in the region to reach a political solution, CNN's Matthew Chance reported from Moscow.

"If a Russian troop withdrawal materializes, it would put President Assad under pressure to finally seriously negotiate a peaceful political transition in Geneva that would ensure the continuation of a Syrian state," said German Foreign Minister Frank-Walter Steinmeier.

Said CNN's Chance: "You can't ignore the timing of this and the symbolism."