Syrian troops battling ISIL crossed to the eastern bank of the Euphrates River in Deir Az Zor on Monday, securing their hold on the war-torn city but threatening a potential standoff with US-backed forces operating nearby.

Russian-backed Syrian forces are trying to tighten the noose on Islamic State of Iraq and the Levant (ISIL, also known as ISIS) fighters who are still inside the city on the river's western bank.

The Syrian army sealed off Deir Az Zor on three sides as of Monday, but ISIL still controls eastern districts along the river, which both the group and civilians had used as an escape route.

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On Monday, elite Syrian forces crossed the river, Russia's defence ministry said.

"Today, Syrian government forces - reinforced by a unit of the 4th Armoured Division and with the support of Russian aviation - crossed the Euphrates River in the Deir Az Zor region," a ministry statement said.

It said "shock troops" had already captured several villages on the river's eastern bank from ISIL and were pushing further east.

A commander in a militia of the US-backed Syrian Democratic Forces (SDF) confirmed Syrian army units had crossed and said his fighters were ready to drive them back.

"If there are clashes between us and them - we're ready for those if the forces of the regime don't go back to the other bank," Ahmed Abu Khawla of the SDF's Deir Az Zor military council said.

Intense air raids

Rami Abdurrahman, head of the UK-based Syrian Observatory for Human Rights war monitor, said the advance across the river was preceded by intense air raids on the eastern bank.

"Even if the pro-government [forces] keep up their advance in the city, it will mean nothing if they don't control the eastern bank," Abdurrahman said.

The US and Russian-backed offensives against ISIL have stayed out of each other's way with the Euphrates often acting as a dividing line. Talks have been under way to extend a formal demarcation line, officials have said.

The Syrian army has recently made major gains in Deir Az Zor.

The Euphrates slices diagonally across the province, an oil-rich eastern region of Syria bordering Iraq.

Until Monday, Syrian troops had only fought west of the Euphrates, while the SDF waged a rival offensive against ISIL east of the river.

The SDF has captured more than 500 square kilometres in northeastern parts of the province, according to the US-led coalition that is providing air cover.

To prevent the two operations from clashing, the coalition, the SDF, Syria's government, and Russia have agreed on a "de-confliction line" in northeast Syria.

That line runs from the neighbouring province of Raqqa and southeast along the Euphrates to Deir Az Zor.

Coalition spokesman Colonel Ryan Dillon declined to say whether the Syrian army crossing the river violated the de-confliction line.

Dillon said last week the US-backed fighters had no plans to go into the city.

READ MORE: Syrian army readies final fight to capture Deir Az Zor

Meanwhile, Deir Az Zor's military airport in eastern Syria, which the Syrian army recaptured this month from ISIL, began functioning again on Monday for the first time in nearly a year, Syrian state media said.

Syrian government forces and their allies broke ISIL's three-year siege of Deir Az Zor earlier this month, reaching the government-held enclave in the city and the adjacent airbase.

The UN estimates about 93,000 people were living in "extremely difficult" conditions in government-held parts of Deir Az Zor during ISIL's siege and were supplied by air drops to the base.