BEIRUT (Reuters) - Syrian troops crossed to the eastern side of the Euphrates in Deir al-Zor on Monday, state media and a monitoring group said, increasing their presence in an area where U.S.-backed militias have also advanced.

The rival forces are conducting offensives against Islamic State and have generally stayed out of each other's way, with the river often acting as a dividing line.

However, incidents this year have raised tension between the government side, backed by Russia, and the U.S.-backed forces.

Talks have been under way to extend a formal demarcation line, officials have said.

A commander in a militia of the U.S.-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 al-Zor military council said.

Russia's foreign ministry said on Friday Syrian government forces crossed the river for the first time in their offensive against the jihadist group in Deir al-Zor province.

Monday's crossing took place near a southern suburb of the city seized by the army on Saturday, the British-based Syrian Observatory for Human Rights said.

Syrian state news agency SANA said heavy fighting took place against Islamic State in the area.

The militant group said via its online Amaq news agency that it had deployed at least two suicide car bombs against government forces.

The convergence of the Syrian army offensive from the west and the SDF operation from the east has led to increased tensions.

The SDF said they came under attack from Syrian forces and Russian jets backing them on Saturday, after Abu Khawla said they would not allow the army to cross the river and would consider shots fired in their direction as an attack.

The SDF has advanced to within kilometres of the river, while the Syrian army has retaken much of the city, most of it on the western side.

Story continues

President Bashar al-Assad has vowed to recapture all of Syria. Assad controls the main urban centres in the west of the country.

The SDF, dominated by the Kurdish YPG militia, controls much of Syria's northeast.

Syrian rebel groups which have fought against Assad since 2011 hold pockets of territory in western Syria.

Islamic State's shrinking territory includes much of oil-rich Deir al-Zor province.

(Reporting by John Davison and Ellen Francis; Editing by Janet Lawrence and John Stonestreet)