BEIRUT (Reuters) - U.S.-backed militias said they captured Syria’s largest oil field on Sunday, pressing their assault against Islamic State in the east of the country.

A road sign welcomes people to the town of Deir al-Zor in Syria September 20, 2017. Picture taken September 20, 2017. REUTERS/Omar Sanadiki

The Syrian Democratic Forces (SDF) said they took al-Omar field on the eastern bank of the Euphrates river in the early hours. “Our forces managed to liberate the fields without notable damages,” said Lilwa al-Abdallah, spokeswoman for the offensive in Deir al-Zor province.

The jihadists holed up in buildings in a nearby district, where the SDF was trying to hunt them down, she said.

With U.S.-led jets and special forces, the SDF has been battling in Deir al-Zor bordering Iraq. The alliance of Kurdish and Arab militias has focused on territory east of the river, which bisects the oil-rich province.

The Syrian army, with Russian air power and Iran-backed militias, has been waging its own separate offensive against Islamic State, mostly to the west of the river.

The U.S.-led coalition and the Russian military have been holding deconfliction meetings - to prevent clashes between planes and troops - though the two offensives have sometimes come into conflict.

Islamic State has lost vast territory across Syria, and has now come under attack in its last footholds in a strip of the Euphrates valley and the desert in Deir al-Zor.

The SDF declared victory over the jihadists in their former headquarters in Raqqa city this week. SDF fighters would now move to the frontlines in Deir al-Zor, speeding up the battle in eastern Syria.

Last month, the Kurdish-led militias captured a major natural gas field upstream of Sunday’s advance.

Al-Omar oil field lies some 10 km (6.21 miles) north of the town of al-Mayadin, which government troops and their allies took earlier this month. The town had turned into a major base for Islamic State militants after the U.S.-backed offensive drove them out of Raqqa.

The Syrian Observatory for Human Rights said Islamic State fighters who had withdrawn from the oil field mounted a counter-attack overnight against government forces. The militants made some gains around al-Mayadin, the Britain-based monitor said.

But a Syrian military source denied this, saying there was no significant attack and fighting raged on at the same pace.

Any attack by the Islamic State militants there was a “desperate attempt”, the source said. “The Syrian Arab Army is attacking, hitting Daesh positions...and advancing,” the source said, using the Arabic acronym for Islamic State.