Iraqi security forces say heavy fighting is taking place between troops and fighters belonging to the Islamic State of Iraq and the Levant (ISIL) group in the province of Anbar, with reports of progress in Ramadi and losses in Fallujah.
The sources say at least 27 soldiers have been killed in the south of Fallujah in different attacks.
An ISIL raid in the Nuaimiya area in the city's southeast killed 22 Iraqi soldiers, including a captain, the sources said on Saturday, adding that another seven had been killed in a village nearby.
The attacks were followed by clashes between ISIL and the Iraqi military.
READ MORE: Al Jazeera's comprehensive coverage of ISIL's impact on the Middle East
Health personnel in the city told Al Jazeera that seven civilians had been killed when their neighbourhood was shelled by the army.
Iraqi medical sources say the shelling targeted southern neighbourhoods in Fallujah, damaging shops and homes.
Witnesses say people in the city have run out of basic supplies and, owing to the power outages, they are fast running out of fuel for generators.
The Iraqi military has besieged Fallujah for a year in an attempt to force out ISIL fighters.
Meanwhile, in Ramadi, intense firefights are occurring between troops and ISIL fighters near the centre of the city, Iraqi security forces say.
The forces say they have managed to advance thanks to air strikes carried out by the US and its allies.
As part of an operation launched on Tuesday, the troops have pushed deeper into the heart of the last remaining district held by ISIL, despite being slowed by bombs and booby traps, army spokespersons said.
Related: Displaced Iraqis seek help to return home
Soldiers advanced overnight in the Hoz neighbourhood that houses the provincial government compound, Brigadier Yahya Rasool, the joint operations command spokesman, said on Saturday.
Most remaining civilians in the ISIL-held central district have taken shelter in Ramadi's hospital, knowing that the army will not target it, he said.
Ramadi, the provincial capital, lies in the fertile Euphrates River valley, just two hours' drive west of Iraq's capital Baghdad.
Recapturing Ramadi, which fell to ISIL in May, would be one of the most important victories achieved by government forces since the fighters swept across a third of Iraq in 2014.
Source: Al Jazeera and agencies