The first attack happened at dawn on Wednesday when 10 suicide bombers belonging to ISIL, also known as ISIS, hit the town of Kubaisah before storming the nearby village of Al Sejar, and then attacked an army convoy to the south of Fallujah at Amiriyat al-Fallujah with roadside bombs, military sources told Al Jazeera.
After more than a week of operations aimed at retaking Fallujah, which lies just 50km west of Baghdad, the Iraqi army - made up of the military, police and Shia units, and backed by air power from a US-led coalition - has been unable to reach the city centre.
The overall commander of the Fallujah operation, Lieutenant-General Abdelwahab al-Saadi, told Al Jazeera that while the Iraqi army had slowed its advance, it was still at the fringes of Fallujah.
"We are here in Naimiyah district and operations are ongoing, and the advance towards the centre of Fallujah is continuing too," he said.
The Iraqi government has blamed ISIL for the slow progress by using human shields and preventing civilians from leaving the city.
"It would've been possible to end the battle quickly if protecting civilians wasn't one of the foundations of our plan," Haider al-Abadi, Iraq's prime minister, said in comments broadcast by state television.
Al Jazeera's Omar Al Saleh, reporting from Erbil, said the situation was calm on the southern front of Fallujah after Wednesday's bloody clashes.
"ISIL seems to be well entrenched and has seeded the area with IEDs, so that might explain why Iraqi forces and its militias have been slow to advance."
He quoted Iraqi commanders as describing ISIL's latest actions as "desperate" and as those of a group in its "last stages."
Since the start of the operation on May 22-23, Iraqi commanders have claimed to have killed dozens of ISIL fighters but remain hesitant about releasing their own casualty figures.
However, a member of the security forces posted outside Najaf's Valley of Peace, where many from Iraq's Shia majority bury their dead, told the AFP news agency that it had "received about 70 fighters, probably a bit more".
Officials in Basra said the southern province had lost 26 fighters from Shia units belonging to the Hashed al-Shaabi umbrella group.
Medics also reported many wounded from the battle for Fallujah. Since Monday, just two of Baghdad's hospitals received 97, AFP reported.
The operation for Fallujah has come at a dire human cost, with thousands of civilians trapped between ISIL fighters and the advancing Iraqi army.
Timeline: The battle for Fallujah
Up to 50,000 people are still stuck in the centre of the city on Thursday, struggling with dwindling water and food supplies.
No aid has reached Fallujah since September last year and residents have been living on dates, dirty water from the Euphrates and animal feed.
Analyst on battle for Fallujah: 'This is not a strategy to defeat ISIL'
Lise Grande, deputy special representative of the United Nations Assistance Mission for Iraq, told Al Jazeera there was a dramatic story unfolding on the ground with at least "50,000 Iraqis at grave risk".
"ISIL have moved many families to the centre of town where they're a kind of human shield," she said citing informants on the ground.
"There is widespread food deprivation. Medicines haven't made it into Fallujah for months. We know that people no longer have access to clean drinking water and they're forced to drink out of the irrigation canals. We're worried that there might even be a cholera outbreak because of this."
Fallujah is one of only two major Iraqi cities - the other being Mosul - still controlled by ISIL.
Armed Sunni Arab groups in Fallujah fought the US occupation of Iraq and the Shia-led authorities that replaced Iraqi leader Saddam Hussein.
The city on the Euphrates River had a pre-war population of about 300,000.
Known as the City of Minarets and Mother of Mosques, it was badly damaged in two assaults by the US army in 2004.