By Denis Dyomkin and Suleiman Al-Khalidi

MOSCOW/GENEVA (Reuters) - President Vladimir Putin announced out of the blue on Monday that "the main part" of Russian armed forces in Syria would start to withdraw, telling his diplomats to step up the push for peace as U.N.-mediated talks resumed on ending the five-year-old war.

Damascus rejected any suggestion of a rift with Moscow, saying President Bashar al-Assad had agreed on the "reduction" of Russian forces in a telephone call with Putin.

Western diplomats speculated that Putin may be trying to press Assad into accepting a political settlement to the war, which has killed 250,000 people, although U.S. officials saw no sign yet of Russian forces preparing to pull out.

The anti-Assad opposition expressed bafflement, with a spokesman saying, "Nobody knows what is in Putin's mind".

Russia's military intervention in Syria in September helped to turn the tide of war in Assad's favor after months of gains in western Syria by rebel fighters, who were aided by foreign military supplies including U.S.-made anti-tank missiles.

Putin made his surprise announcement, that came with no advance word to the United States, at a meeting with his defense and foreign ministers.

Russian forces had largely fulfilled their objectives in Syria, Putin said. But he gave no deadline for the completion of the withdrawal and said forces would remain at a seaport and airbase in Syria's Latakia province.

In Geneva, United Nations mediator Staffan de Mistura told the warring parties there was no "Plan B" other than a resumption of conflict if the first of three rounds of talks that aim to agree a "clear roadmap" for Syria failed to make progress.

Putin and U.S. President Barack Obama spoke by phone on Monday about Syria, with the Kremlin saying the two leaders "called for an intensification of the process for a political settlement" to the conflict.

The White House said Obama welcomed the reduction in violence since the beginning of the cessation of hostilities but "underscored that a political transition is required to end the violence in Syria.”

Story continues

A U.S. official, speaking on condition of anonymity, said Washington was encouraged by Putin’s announcement but that it was too early to say what it means, whether he will carry it out and what may have motivated it.

Putin said at the Kremlin meeting that he was ordering the withdrawal from Tuesday of "the main part of our military contingent" from the country.

"The effective work of our military created the conditions for the start of the peace process," he said. "I believe that the task put before the defense ministry and Russian armed forces has, on the whole, been fulfilled."

With the participation of the Russian military, Syrian armed forces "have been able to achieve a fundamental turnaround in the fight against international terrorism", he added.

'COMPLETE COORDINATION'

Kremlin spokesman Dmitry Peskov said Putin had telephoned the Syrian president to inform him of the decision, but the two leaders had not discussed Assad's future, the biggest obstacle to reaching a peace agreement.

The move was announced on the day U.N.-brokered talks involving the warring sides in Syria resumed in Geneva.

In Damascus, the Syrian presidency said in a statement that Assad had agreed to the reduction in the Russian air force presence, and denied suggestions it reflected a difference between the two countries

"The whole subject happened in complete coordination between the Russian and Syrian sides, and is a step that was carefully and accurately studied for some time," the statement said, adding that Moscow had promised to continue support for Syria in "confronting terrorism."

Syria regards all rebel groups fighting Assad as terrorists.

Rebels and opposition officials alike reacted skeptically.

"I don't understand the Russian announcement, it's a surprise, like the way they entered the war. God protect us," said Fadi Ahmad, spokesman for the First Coastal Division, a Free Syria Army group fighting in the northwest.

Opposition spokesman Salim al-Muslat demanded a total Russian withdrawal. "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," he said.

A European diplomat was also skeptical. "It has the potential to put a lot of pressure on Assad and the timing fits that," the diplomat said.

"However, I say potentially because we've seen before with Russia that what's promised isn't always what happens."

MOMENT OF TRUTH

The Geneva talks are the first in more than two years and come amid a marked reduction in fighting after last month's "cessation of hostilities," sponsored by Washington and Moscow and accepted by Assad's government and many of his foes.

Russia's U.N. ambassador, Vitaly Churkin, confirmed some forces would stay in Syria. "Our military presence will continue to be there, it will be directed mostly at making sure that the ceasefire, the cessation of hostilities, is maintained," he told reporters at the United Nations in New York.

But he added, "Our diplomacy has received marching orders to intensify our efforts to achieve a political settlement in Syria."

Speaking before Putin's announcement, de Mistura said Syria faced a moment of truth, as he opened talks to end a war which has displaced half the population, sent refugees streaming into Europe and turned Syria into a battlefield for foreign forces and jihadis.

The limited truce, which excludes the powerful Islamic State and Nusra Front groups, is fragile. The warring sides have accused each other of multiple violations and they arrived in Geneva with what look like irreconcilable agendas.

The Syrian opposition has said the talks must focus on setting up a transitional governing body with full executive power, and that Assad must leave power at the start of the transition. Damascus has said Assad's opponents are deluded if they think they will take power at the negotiating table.

(Additional reporting by Phil Stewart, Arshad Mohammed, Eric Beech, Michelle Nichols, Tom Miles, Tom Perry, Stephanie Nebehay and Jack Stubbs; Writing by Dominic Evans, David Stamp and Peter Cooney; Editing by Angus MacSwan, Toni Reinhold)