The town lies almost 300 km (190 miles) from Deir Al Zor city in the east, the current focus of the government offensive, with Russian jets and militias, against IS.
Al-Abdullah said SDF forces were working to expel the militants from a nearby neighborhood where they had taken refuge.
The capture of al-Omar gives the Kurdish-led SDF control over a vital strategic asset that could serve to give it leverage in any future negotiations over the status of Kurds in Syria and to fund the fledgling autonomous region they are building in northeastern Syria.
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Syria's largest oil field was seized from the Islamic State terror group on Sunday by the USA -led coalition, dealing another blow to the extremist group after the loss of its de-facto capital last week.
Little life is left in Al-Mayadeen, located south of Deir Ezzor in Syria, after Syrian government forces and their allies captured the town on October 15.
The SDF declared the "total liberation" of Raqqa on Friday, which for more than three years was the de facto capital of ISIS. The oil industry was a pillar of the Syrian economy before the conflict in 2011.
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The Kurdish-led Syrian Democratic Forced, with air support from the US -led coalition, said it captured the Al-Omar field in a "swift and wide military operation", adding that some militants have taken cover in oil company houses nearby, where clashes are underway.
Syrian troops and allied forces regained control of Al Qaryatayn town "after eliminating terrorist Daesh (IS) groups that had infiltrated it", state media said on Saturday.
The government lost the al-Omar field to other insurgents in 2013. But Dillon declined to say whether U.S. Special Operations forces deployed in Syria alongside the SDF had participated in the operation. "They had been shot dead or executed with knives", Abdelrahman said.
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Syria observers have said the race between the US-backed fighters and the Russian- and Iranian-backed Syrian government forces is likely to be a source of direct confrontation in the absence of a political agreement. Most of the territory the group once held has been seized by an array of Syrian and Iraqi forces.