Iraqi forces faced tough resistance from the Islamic State group Tuesday as they attempted to enter the centre of Fallujah, where there were mounting fears for thousands of trapped civilians.

A day after announcing a push into the jihadist stronghold, forces led by Iraq's elite counter-terrorism service had some way to go before retaking the city.

After thrusting toward Fallujah from three directions on Monday, their biggest advance was from the south, where they pushed into the suburb of Naimiyah.

Lieutenant General Abdelwahab al-Saadi, the overall commander of the Fallujah operation, said IS fighters mounted a fierce counter-attack on the area early on Tuesday.

"There were around 100 fighters involved, they came at us heavily armed but did not use car bombs or suicide bombers," he told AFP.

Saadi said Iraqi forces in the area, which also include police and army units, were eventually able to repel the attack, killing 75 jihadists.

He did not give a figure for losses on the pro-government side.

Officers said US-led coalition and Iraqi air support was instrumental in repelling the attack and added that ground forces had now resumed their advance.

The Pentagon said the Fallujah offensive was "tough".

"The past two days have shown" that IS "intends to put up a fight for it," said spokesman Jeff Davis.

Fallujah, which lies on the Euphrates River west of Baghdad, was lost from government control months before IS swept across large parts of Iraq in June 2014 and is an emblematic bastion for the jihadist group.

Iraqi forces have been sealing off Fallujah for months and those still in city -- IS fighters and civilians alike -- have nowhere to go.

- Families used as 'shields' -

Anbar capital Ramadi was almost levelled when Iraqi forces retook it a few months ago but many more civilians -- most estimates say around 50,000 -- are trapped inside Fallujah.

The UN's refugee agency (UNHCR) spoke of "reports of several hundred families being used as human shields by ISIL (IS) in the centre of Fallujah."

UN deputy representative to Iraq Lise Grande described the reports as "credible" and said the families being pushed into the city centre were at "extreme risk".

A Fallujah resident contacted by AFP by telephone said many civilians were now eager to see the security forces recapture the city but that there was fear of what the jihadists might do as defeat loomed.

"There is some discontent among the people because we haven't seen the Iraqi forces enter the centre yet," said the resident, who gave his name as Abu Mohammed al-Dudaim.

"Their treatment of the people is getting worse and worse every day. There is a feeling of panic among them it seems.

"Dash is angry because they don't feel supported," he said, using an Arabic acronym for IS.

"Yesterday, they were rounding up young men from several parts of the city -- we think maybe around 100 of them -- and taking them to an unknown location," he said.

Officers in the Iraqi forces say IS has been forcibly recruiting men and ever younger boys to man its defence.

A 40-year-old woman reached by the Norwegian Refugee Council (NARC) inside Fallujah painted a dire picture of the conditions.

"The stocks in the hospitals are running low. There is no medicine for ordinary people. The doctor is affiliated with IS and he refuses to help ordinary people," the aid group quoted her as saying.

"Instead of providing adequate treatment, doctors often simply amputate a patients arms or legs if they are in pain. There are no anaesthetics left."

- 'Need for safe exits' -

Thousands of civilians have escaped IS-controlled areas since the start of the operation to retake the city on May 22-23 but nearly all of them were from outlying areas.

The 50,000 civilians still believed trapped in the city centre would have to dodge IS booby-traps and incoming shelling from pro-government forces to reach safety.

"People who managed to flee have told us of extreme hunger and starvation. We haven't been able to see this for ourselves or assist people inside the town, and we are extremely concerned about the full extent of the terrors unfolding there," said Nasr Muflahi, the NRC's Iraq director.

IS has come under mounting pressure on the battlefield in recent weeks, with Kurdish forces also gaining ground in the north in a two-day operation that wound up on Monday east of Mosul, the jihadists' other urban bastion in Iraq.

On the back foot in Iraq, IS has tried to retain the initiative in neighbouring Syria with an offensive against non-jihadist rebels in the north of Aleppo province along the Turkish border.

That fighting, which the Syrian Observatory for Human Rights said intensified on Tuesday, has also trapped tens of thousands of civilians.

"The situation is absolutely unsustainable and unacceptable for this population," said Pablo Marco, regional head of Doctors Without Borders (MSF).