Russian President Vladimir Putin has ordered the withdrawal of the majority of Russian troops in Syria starting Tuesday, saying their task has been "completely fulfilled."

Putin said he hoped the pullout will be a stimulus for a political resolution of the conflict.

"The task presented to the Defence Ministry and the armed forces has been completely fulfilled," Putin told Defence Minister Sergei Shoigu on Monday, the same day representatives of the Syrian government and opposition struggled to agree on President Bashar al-Assad's future at the start of renewed peace talks in Geneva.

"Thus I order the defence minister to begin withdrawing the majority of our troops from the Syrian Arab Republic tomorrow," Putin said in comments carried by state news agency TASS.

He emphasized that Russia's airbase in the Syrian province of Latakia and its naval facility in the province of Tartus should still be protected despite the withdrawal.

Putin also said the withdrawal had the consent of al-Assad, a longtime ally whom Russia has supported with air campaign since September.

Russia's intervention in support of al-Assad's overstretched forces is believed to have marked a turning point in the war.

A statement from the Syrian presidential palace said that Moscow had vowed to continue backing Damascus in its fight against terrorism, according to Syrian state media.

"The Syrian and Russian sides agreed during a telephone conversation between the two presidents ... Assad and Putin to reduce the numbers of the Russian air force in Syria," the statement read.

The move followed the "continued successes" of the Syrian military backed by Russian air power "in the fight against terrorism," it said, and what it called "the return of security and safety" to many areas in Syria.

Shoigu told Putin that Russian forces have eliminated more than 2,000 rebels who had come to Syria from Russia. He said that included 17 rebel field commanders.

Russia and the United States brokered a ceasefire in Syria last month that has reportedly been mostly observed.

"Russia's biggest risk in the Syria operation was to be dragged into a long-term military conflict. As we see, that did not happen," prominent Russian political analyst Yevgeny Minchenko told the Interfax news agency.

"The Russian military demonstrated well enough its diverse capabilities," Minchenko said.

US President Barack Obama spoke with Putin by phone on Monday, the White House said. They discussed Putin's announcement and next steps required to fully implement the cessation of hostilities.

"Obama welcomed the much-needed reduction in violence since the beginning of the cessation," a White House statement said. But Obama also stressed to Putin that continuing military actions by Syrian regime forces risk undermining both the ceasefire and the UN-led political process.

Obama also noted some progress on humanitarian assistance efforts in Syria but emphasized the need for regime forces to allow access for aid deliveries to the agreed-upon locations, notably Daraya.

The United States has waged a bombing campaign against some rebel groups in Syria while supporting others in their fight against al-Assad.

Syrian opposition said they wanted to know the extent of the Russian withdrawal.

"If there is a withdrawal, we want to know if it includes halting the aerial bombardement. If it is the case then this will change the crisis as a whole," said Munzer Makhous, a spokesman of the opposition's Saudi-based High Negotiations Committee (HNC).

"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," said Salem Al Meslet, another HNC spokesman.

When asked why Russia had chosen to withdraw now, Russian UN ambassador Vitaly Churkin said: "Because we are in the political mode now ... Our diplomacy has received marching orders to intensify our efforts to achieve a political settlement in Syria."

"The international effort to fight terrorism is going to continue," Churkin added. "We have done what we have done, we think that our forces have operated very effectively."

He added that Russia would now focus on maintaining the current ceasefire in Syria.

Tuesday marks the fifth anniversary of the start of the Syrian uprising, which has left more than a quarter of a million people dead and driven millions of Syrians from their home.

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