At least 28 Iraqi soldiers have been killed in suicide attacks blamed on the Islamic State of Iraq and the Levant (ISIL) group in Anbar.

Iraqi government officials said one car bomb hit an army barracks on Thursday in the provincial capital Ramadi, where fighting has continued for months despite the Iraqi government's claim that it controls 95 percent of the city.

The second attack targeted a government base in Fallujah, the other major ISIL-controlled city under siege by Iraqi forces, the officials said.

Iraqi forces have been trying to clear areas of Anbar controlled by ISIL, which has seized territory in Iraq and Syria, but their advance has been slowed down by suicide attacks.

In Ramadi's Sijariya district, government forces said 50 percent of the city is now cleared.

Backed by air support from the US-led international coalition and Iraq's air force, counterterrorism troops advanced towards the centre of Sijariya.

The Ramadi police force also joined the push.

"Our forces advanced into Sijariya district, which is the last stronghold of Daesh (ISIL) and its fortified place" Lieutenant-Colonel Muhannad al-Timmimi, from Iraq's elite Special Forces, told Reuters news agency.

He said government forces had killed 37 ISIL fighters, destroyed two car bombs and removed 225 other bombs.

Flashpoint Ramadi

ISIL fighters have been pushed to Ramadi's eastern suburbs, but almost all of the city, which was targeted by US-led air strikes, remains off-limits to its nearly half a million displaced residents, most of whom fled before the army advance.

Military sources said the counterterrorism forces had also attacked positions in Husaiba al-Sharqiya, 10km east of Ramadi.

ISIL fighters have left Ramadi's streets and buildings booby-trapped with bombs, hampering efforts to rebuild the city two weeks after Iraq's elite counterterrorism forces claimed victory, officials said.

Ramadi is the capital of the mainly Sunni Arab Anbar province. The government said it would be handed over to the local police and to a Sunni tribal force once it was secured.

Ramadi was ISIL's biggest prize of 2015, abandoned by government forces in May in a major setback for Baghdad and for the Iraqi troops that have been trained by the US since the overthrow of Saddam Hussein in 2003.

Siege of Fallujah

Elsewhere in Anbar, Iraqi security forces have completely cut off Fallujah and supplies of food and other basic necessities are running out, raising fears of a humanitarian crisis.

In a telephone interview with Al Jazeera on Thursday, a Fallujah resident trapped inside the town said a 50kg bag of wheat costs as much as $900.

"Some residents had to sell their cars just to buy wheat for their families. There is no source for income for Fallujah's residents any more. Medicine ran out from pharmacies and clinics. Last month 10 people died for the lack of insulin," he said.

The resident spoke to Al Jazeera at personal risk as ISIL has banned all communication with the media.

One Iraqi military analyst said the Baghdad government has little choice other than to lay siege to Fallujah.

"There are no alternative plans. All the available plans by security forces are either to break into Fallujah, causing huge civilian casualties, or to shell it with mortars and air strikes, potentially causing catastrophic damage to basic infrastructure and human lives," Waltham al-Hashimi, a defence analyst, told Al Jazeera.

So far aid agencies including the UN have not commented publicly on the siege of Fallujah, Al Jazeera's Imran Khan, reporting from Baghdad, said.

No journalists are allowed in either by the government or ISIL, but what sources say suggests the situation remains dire.

"It might not be a humanitarian disaster yet, but that could be only a matter of time," he said.