MOSCOW: Russia warned the United States it would target areas in Syria where U.S. special forces and U.S.-backed militia were operating if its own forces came under fire from them, which it said on Thursday had already happened twice.

Russia was referring to the Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab militias fighting with the U.S.-led coalition, which Moscow said had diverted from the battle for control of Raqqa to Deir al-Zor, where Russian special forces are helping the Syrian army push out Daesh (ISIS) militants.

The Russian Defence Ministry said the SDF had taken up positions on the eastern banks of the Euphrates with U.S. special forces, and had twice opened fire with mortars and artillery on Syrian troops who were working alongside Russian special forces.

"A representative of the U.S. military command in Al Udeid (the U.S. operations centre in Qatar) was told in no uncertain terms that any attempts to open fire from areas where SDF fighters are located would be quickly shut down," Major-General Igor Konashenkov said in a statement.

"Fire points in those areas will be immediately suppressed with all military means."

The Russian warning underscores growing tensions over Syria between Moscow and Washington. While both oppose Daesh, they are engaged, via proxies, in a race for strategic influence and potential resources in the form of oilfields.

In eastern Syria's Deir al-Zor province, Daesh is battling two separate offensives with the SDF on one side and the Syrian army and its allies on the other.

In a sign of escalating tensions, the Russian Defence Ministry this week accused U.S. spies of initiating a militant offensive against government-held parts of north-west Syria on Tuesday.

The ministry, in a Wednesday evening statement, said 29 Russian military policemen had been surrounded by militants as a result and that Russia had been forced to break them out in a special operation backed with air power.

"According to our information, U.S. intelligence services initiated the offensive to halt the successful advance of government troops to the east of Deir al-Zor," said Colonel-General Sergei Rudskoi.

The Syrian army, backed by Russian war planes, has captured about 100 km of the west bank of the Euphrates this month, reaching the Raqqa provincial border on Wednesday, the Syrian Observatory for Human Rights reported.

Syrian troops also crossed to the eastern side of the river on Monday where the SDF has been advancing.

The convergence of the rival offensives has increased tensions in Deir al-Zor.

The U.S.-backed militia said on Saturday they had come under attack from Russian jets and Syrian government forces, something Moscow denied.

On Monday, the SDF warned against any further Syrian army advances on the eastern riverbank, and Russia's Defence Ministry said on Tuesday that the waters of the Euphrates had risen as soon as the Syrian army began crossing it, suggesting this could only have happened if upstream dams held by the U.S.-backed opposition had been opened.