WASHINGTON (AFP) - Islamic State in Iraq and Syria (ISIS) snipers are targeting humanitarian corridors established by Iraqi security forces to relieve suffering in the ISIS-held city of Fallujah, a Pentagon official said on Friday.

Baghdad-based military spokesman Colonel Steve Warren said the shooters were preventing residents from escaping Fallujah, which is only about 50km west of Baghdad and is facing major shortages of basic supplies including medicine.

"We know that the Iraqis have attempted on several occasions to open up humanitarian corridors to allow some of those civilians to come out," Warren told Pentagon reporters in a video call.

"Those have met with generally not much success. ISIL has done things like set up snipers to cover down on those corridors, to kill people as they're trying to get out. So that has really discouraged their use," he added, using an acronym for the ISIS group.

Warren later said Iraqi forces had tried to set up three corridors, but these have been all but abandoned because of the snipers.

"Word must have spread because no civilians have tried to use the corridors in the last few weeks," he said.

Anti-government fighters took control of Fallujah in early 2014 during unrest that broke out after security forces demolished a protest camp farther west, and it later became an ISIS stronghold.

Warren said Iraqi security forces now "generally" surround Fallujah and have begun to slowly "chip away" at it.

"This is the very first city that ISIL gained control of," he said.

"ISIL's been there for more than two years, so they are dug in and dug in deep. This is a tough nut for us to crack here. This is a tough nut for the Iraqis to crack."

US forces are training and advising Iraqi partners as they try to repel ISIS militants from the country.

The Pentagon says the ISIS group is losing ground, and the militants have suffered major defeats in Iraq, including the loss of the cities of Heet and Ramadi.

But they remain in control of Iraq's second-largest city Mosul and it is not clear when Iraqi troops will mount an assault to retake it.

Warren said there was no "no military reason" for Iraqi forces to liberate Fallujah before they could tackle Mosul.

About half of Iraq's security forces are focused on protecting Baghdad, where ISIS fighters claimed responsibility for a string of suicide attacks this week.

At least 94 people were killed in three blasts in Baghdad on Wednesday, the deadliest day in the Iraqi capital this year.