(Reuters) - U.S.-backed Syrian militias said Russian warplanes struck their positions in Deir al-Zor province on Monday, near a major natural gas field they seized from Islamic State in recent days.

The Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab militias fighting with the U.S.-led coalition, said the attack killed one of its fighters and injured two others.

There was no immediate comment from Moscow.

Russia and the United States back separate offensives against Islamic State militants in eastern Syria, with both advancing in oil-rich Deir al-Zor bordering Iraq.

The assaults converged on Islamic State from opposite sides of the Euphrates river that bisects Deir al-Zor, Islamic State's last major foothold in Syria.

With Russian air power and Iran-backed militias, Syrian troops closed in from the west. The SDF has advanced from the east with U.S. jets and special forces, capturing the large gas field on the river's bank this week.

"Russian and regime forces have mounted a treacherous attack against our forces...with artillery and aircraft," the SDF statement said.

"We will not stand by with our arms crossed and we will use our legitimate right to self-defence," it said.

Russian and U.S. battles against Islamic State in Syria have mostly stayed out of each other's way, with the Euphrates often acting as a dividing line. But their offensives have at times raised fears of clashes that could stoke tensions between the competing world powers.

Last week, the Pentagon accused Moscow of bombing SDF positions on the eastern side of the river. Russia denied this, warning the United States it would target the SDF if its own forces came under fire.

Colonel Ryan Dillon, spokesman for the U.S.-led coalition, has denied that Washington was racing with Moscow over Deir al-Zor. Contacts were increasing to avoid confrontation, he said.