By William Maclean

DUBAI (Reuters) - Moscow's military intervention in Syria will have "dangerous consequences", escalating sectarian war there and inspiring militants from around the world to join in, senior Saudi Arabian officials told Russia's leaders on Sunday, a Saudi source said.

The message, twinned with a pledge of support for moderate foes of Syrian President Bashar al-Assad, Russia's ally, signals Saudi suspicions about Moscow's motives in entering a 4-1/2 year war in which some 250,000 people have been killed and some 11 million, or half the population, driven from their homes.

"The Russian intervention in Syria will engage them in a sectarian war," the source said on Monday, adding that the kingdom "warns of the dangerous consequences of the Russian intervention".

"The Saudis will continue strengthening and supporting the moderate opposition in Syria," he added.

The source said he was citing positions outlined by Defence Minister and Deputy Crown Prince Mohammed bin Salman and Foreign Minister Adel al-Jubeir during meetings with President Vladimir Putin and Foreign Minister Sergei Lavrov on Sunday in the Russian Black Sea resort of Sochi.

The bloodshed in Syria, part of a broader struggle for regional supremacy between Sunni Muslim Saudi Arabia and Shi'ite Iran, has enflamed sectarian divisions across the Middle East and drawn religiously motivated foreign fighters to both sides.

Moscow's intervention has infuriated the kingdom and other foes of Assad who say the Russian air strikes have been hitting rebel groups opposed to the Syrian leader and not just the Islamic State fighters Moscow says it is targeting.

Gulf Arab states suspect the Kremlin's main motive is saving Assad and that counter-terrorism serves as a convenient excuse.

ESCALATION

Saudi Arabia, along with Turkey and Qatar, is a leading supporter of the rebels fighting Assad, who is backed by Iran as well as by Russia. But Riyadh is also worried about the rise of jihadist groups such as Islamic State among the opposition.

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"The recent escalation will contribute in attracting extremists and jihadists to the war in Syria," the Saudi source said, adding that the Kremlin's actions would also alienate ordinary Sunni Muslims around the world.

The Saudis urged Russia to help fight terrorism in Syria by joining the existing coalition comprising more than 20 nations that is battling Islamic State militants, the source said.

He also reiterated that Assad must quit as part of a process agreed at a Syrian conference held in Geneva in June 2012 that set out a path to peace and political transition.

A core element of that plan calls for a future Syrian government to be formed by "mutual consent" of the authorities and the opposition, a stance Washington has said means Assad cannot stay in power.

In remarks to journalists on Sunday about Russia's strikes, Jubeir said he had expressed "our concerns that these operations could be regarded as an alliance between Iran and Russia".

Russia said its main goal is the fight against terrorism, Jubeir added.

(Additional reporting by Vladimir Soldatkin in Sochi; Editing by Gareth Jones)