Since the fall of Mosul in July, ISIL has been losing territory in northern Iraq.
Iraqi forces have launched an offensive to capture one of the last remaining areas under ISIL control in the country.
Two Iraqi infantry divisions and Sunni tribal forces are carrying out the operation in Anbar province, Iraq.
It is believed ISIL fighters are holding 10,000 civilians hostage in the town of Rawa.
Iraqi forces seized several villages from the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), on Saturday in an operation to retake Rawa, the operation’s commander said.
Troops backed by paramilitaries recruited among the region’s Sunni Arab tribes “launched a major offensive to liberate Rumana and the Rawa area”, General Abdelamir Yarallah said.
He later said they had “retaken Rumana and its bridge on the Euphrates” along with 10 other villages.
Rumana is on the north side of the Euphrates just across from al-Qaim, while Rawa, a small town, lies downstream.
Al Jazeera’s Imran Khan, reporting from Baghdad on Saturday, said Iraqi commanders were hopeful the area would be taken quickly.
“We’re not talking about weeks and months; the Iraqis are talking about a few days,” he said.
“The security forces are very confident that they can rout ISIL from one of their last remaining strongholds in Iraq.”
Rawa is the last town still held by ISIL, apart from al-Bukamal just across the border with Syria.
The Euphrates Valley town and nearby villages were bypassed by government troops and allied paramilitaries when they retook the town of al-Qaim on the Syrian border last week.
Haider al-Abadi, Iraq’s prime minister, said on Saturday the Rawa operation aims to “clean open areas in the desert” of western Iraq.
The recapture of Rawa would mark the final battleground defeat of the ISIL group in Iraq and the demise of the “caliphate” declared by Abu Bakr al-Baghdadi in 2014 over large expanses of Iraq and Syria.
“ISIL fully recaptured al-Bukamal, and regime forces and allied militia are now between one to two kilometres from the city limits,” Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights, said on Saturday.
Against this backdrop, al-Abadi said on Saturday that losses from the war against ISIL have cost Iraq $100bn so far.
“Iraq has lost $100bn in the anti-Daesh war, but we have achieved success in three battles; namely liberating the land, maintaining Iraq’s unity and standing up to the threats,” Abadi said during a speech, using the Arabic name for ISIL.