Al-Zawbaei went on to point out that Iraqi ground forces were receiving air support from US -led coalition warplanes, which, he said, had succeeded in destroying "many" ISIS sites in western Anbar.
Deir al-Zour is the center of Syrian oil production and is eastern Syria's largest and most important city.
Iraqi armed forces have re-captured the district of al-Qaim on the border with Syria, driving out the Islamic State, Prime Minister Haider al-Abadi said. The Iraqis, with the support of the global coalition, have now liberated almost all of the territory once held by ISIS in Iraq, they said.
Meanwhile the Syrian government, which is backed by Russian Federation has regained complete control of the eastern city of Deir al-Zor on Friday, representing a huge blow to the jihadists as their last stronghold in Syria crumbles.
Syrian government forces and their pro-government allies first broke the militant group's siege of their part of the city in September in a Russian-backed offensive, and have been advancing against IS positions since then.
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He estimated that there were 1,500 to 2,500 fighters left in Al-Qaim and 2,000 to 3,000 in Al-Bukamal.
The US-led coalition supporting Iraqi forces with air strikes had predicted that the battle for Al-Qaim would be the "last big fight" of the punishing military campaign to dismantle their brutal experiment in statehood.
Troops from the army and the elite Counter Terrorism Service "have started the assault on the centre of Al-Qaim", 7th Division commander Noman Abed al-Zobai said from the scene.
Iraqi forces had surrounded the last of the ISIS fighters in nearby towns Rawa and Romana, as well as surrounding areas north of the Euphrates River on Qaim's outskirts, Rasoul said.
Gaining control of Deir Ezzor was a significant victory for the Syrian government, and followed ISIS' ousting from Raqqa, the de facto capital of the caliphate.