Russian Defence Minister Sergei Shoigu has met Syrian President Bashar al-Assad in Damascus to discuss "military cooperation" in Syria's conflict, a bone of contention between Moscow and Washington.

Shoigu was sent by President Vladimir Putin for the unannounced meeting with Moscow's long-time ally Assad on Saturday, the Syrian state news agency SANA said.

"The talks focused on military cooperation between the two countries and joint action to fight against terrorist organisations on Syrian soil," it said.

In Moscow, the defence ministry said in a statement that the discussions centred on "current questions of military and technical cooperation ... as well as certain aspects of the cooperation in the fight against terrorist groups operating in Syria".

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The visit came as a US defence department spokesman said Pentagon officials in a video conference with Russian counterparts had voiced "strong concerns" over Moscow's alleged bombing of US-backed forces in southern Syria.

US military officials "expressed strong concerns about the attack on the coalition-supported counter-ISIL [Islamic State of Iraq and Levant] forces at the al-Tanaf garrison, which included forces that are participants in the cessation of hostilities in Syria", Pentagon spokesman Peter Cook said.

The Pentagon "emphasised that those concerns would be addressed through ongoing diplomatic discussions on the cessation of hostilities", he said.

US defence officials have said Russian warplanes carried out raids in al-Tanaf targeting a meeting of combatants supported by the US-led coalition that was held to coordinate the fight against ISIL fighters in Syria and Iraq.

The Syrians belonged to the New Syrian Army, trained by the British and the Americans in a coalition camp in Jordan, while the Iraqis were tribal fighters, officials said.

Russia, however, said it had not carried out any strikes targeting opposition forces included in a ceasefire brokered by Washington and Moscow that excludes ISIL, without mentioning al-Tanaf.

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Earlier this month, Shoigu also visited Iran's capital Tehran to take part in talks with his Syrian and Iranian counterparts. Before the meeting, which took place on Iran's initiative, the Russian defence ministry said the officials would be discussing "reinforcing cooperation in the fight with ISIL and al-Nusra terrorist groups".

The Syrian conflict has drawn in world powers, with the US, along with regional powers, largely backing the moderate rebels while Russia began a military offensive in support of the Assad government in September.

A Moscow and Washington-backed ceasefire has been in place since February 27, but a fresh bout of fighting broke out in April that stalled the UN peace talks in Geneva.

More than 280,000 people have been killed since the start of Syria’s war in 2011, and millions have been displaced, the UN estimates.