Iraqi security forces were said to have advanced Tuesday into the center of Ramadi, a strategically important city that has been under ISIL control since May.
"We went into the center of Ramadi from several fronts and we began purging residential areas," said Sabah al-Noman, spokesman of the Iraqi counter-terrorism service. "The city will be cleared in the coming 72 hours," he said.
The fresh push was launched overnight and is aimed at fully recapturing Ramadi, the capital of Iraq's western province of Anbar.
The fighting in Ramadi is led by the elite counter-terrorism force, backed by US-led coalition airstrikes and also supported by forces from the police, the army and Sunni tribes opposed to the armed group.
The Islamic State in Iraq and the Levant (ISIL) has lost several key towns in Iraq since Baghdad and the autonomous Kurdish region started fighting back following the group's devastating offensive 18 months ago.
The Shia-dominated Hashed al-Shaabi paramilitary forces were heavily involved in the battles that led to the recapture of towns such as Tikrit and Baiji but they have remained on the fringes in the battle for Ramadi.
Retaking the city, an insurgent bastion that saw some of the deadliest fighting against US troops a decade ago, would be the Iraqi federal forces' most significant victory so far.
But the advance has not been without setbacks. At the start of the offensive, ISIL mounted an attack with a suicide car bomber against soldiers and Shia militiamen gathered in Bu Dhiyab village north of Ramadi, killing 14 of them, military sources told Al Jazeera. Another 17 soldiers and militiamen were injured in the blast.
In a separate incident, at least eight civilians, including several children, were killed in a series of airstrikes on a residential area north of Ramadi, the sources said.
ISIL fighters have had plenty of time to dig in since they took full control of the city on May 17 after blitzing government forces with wave after wave of car and truck bomb attacks.
The group built tunnels to move without being exposed to the coalition's daily raids but their supply lines were gradually all severed and military officials estimated last week there no more than 300 fighters left in the city.
The breakthrough came earlier this month when Iraq forces broke down ISIL defenses and retook the key southwestern neighborhood of Al-Tameem.
An Iraqi defense ministry spokesman said earlier that ISIL was preventing civilians from leaving Ramadi before the planned attack on the city.
Iraqi military planes on Sunday dropped leaflets on Ramadi, asking residents to leave within 72 hours and indicating safe routes for their exit.
Al Jazeera and wire services