* Incident took place near Deir al-Zor

* Russia denies targeting U.S.-backed SDF

* Rival U.S., Russia-backed campaigns fighting Islamic State (wraps Deir al-Zor, Raqqa strands)

BEIRUT, Sept 25 (Reuters) - U.S.-backed Syrian militias said Russian warplanes struck their positions in Deir al-Zor province on Monday, which Moscow denied, generating friction between two rival campaigns against Islamic State.

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

Major-General Igor Konashenkov of Russia's defence ministry was cited by RIA news agency as issuing a denial, saying Russia was always careful to ensure its air strikes were accurate.

A spokesman for the U.S.-led coalition, Colonel Ryan Dillon, said rounds had hit in the area around the SDF but he could not confirm they were fired by Russia.

A war monitor, the Syrian Observatory for Human Rights, said Russian rounds had not hit the SDF near Deir al-Zor.

The SDF later said it had responded to the source of fire that targeted it from near the city of Deir al-Zor on Monday morning without specifying which forces it had attacked.

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

The assaults are converging on Islamic State from opposite sides of the Euphrates that bisects the province, the jihadists' last major foothold in Syria, with the river often acting as a dividing line.

But their proximity has at times raised the risk of clashes that could stoke tensions between the competing world powers.

With Russian air support and Iran-backed militias, Syrian troops are advancing along the west bank of the river.

A Kurdish commander of the SDF, which has approached along the east bank with U.S. jets and special forces, told Reuters on Monday the alliance expected to completely push Islamic State out of its former Syrian headquarters of Raqqa within a month.

With the Kurdish YPG militia at its forefront, the SDF said last week that, after seizing 80 percent of Raqqa, the battle for the city had entered its final stages.

"In the coming days, the battles will be at their most intense...," said Jihan Sheikh Ahmed, spokeswoman for the offensive. "We expect, under our plan, that we will be able to liberate Raqqa in less than a month."

'RIGHT TO SELF-DEFENCE'

The SDF also captured a large gas field on the Euphrates' bank on Saturday.

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

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

On Monday, Russia's Deputy Foreign Minister Sergei Ryabkov said U.S. policy in Syria was to blame for the death from shelling of Russian general Valery Asapov near Deir al-Zor, which the defence ministry in Moscow announced on Sunday.

Ryabkov called into question U.S. commitment to the fight against Islamic State, accusing it of trying to slow the Syrian army's advance.

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.

Dillon, spokesman for the U.S.-led coalition, said it was communicating with Russia to ensure measures to avoid unintended conflict between the offensives were being followed. (Reporting by Ellen Francis; Additional reporting by Vladimir Soldatkin in Moscow; Editing by John Stonestreet)