"We are advancing on and closing in," Iraqi Defense Ministry spokesman Brigadier Rasool Yahya said, adding, "Our forces have isolated and surrounded the city of Fallujah," Yahya told Qatar's al-Jazeera television.
The first phase of the liberation operation was completed, he said, adding, "We have achieved our objectives."
Leader of Popular Mobilization (Hashid al-Shaabi) units in Anbar Province announced on Saturday the beginning of the second phase of the Fallujah liberation a week since the battle began.
Some 50,000 civilians remain trapped in the city, with the United Nations saying it has reports of people dying of starvation and for refusing to fight for Daesh.
On Saturday, Iraqi forces said they had found underground tunnels dug by the extremists to approach and escape the Fallujah frontline.
Fallujah, located just 50 km (30 miles) west of Baghdad, fell to Daesh in January 2014.
The fall came some six months before the group launched a major offensive in the Arab country and occupied Mosul and other areas.
The Iraqi military recaptured the central city of Ramadi, Anbar's provincial capital, last December.
Daesh raid on Hit repelled
On Sunday, Iraqi forces thwarted an attack by Daesh on the city of Hit in Anbar Province, killing 60 militants.
Fierce clashes erupted between the Iraqi army soldiers and Daesh in which commander of the Iraqi special force Fazel al-Namravi was injured, Iraq's al-Sumaria satellite TV network reported.
According to the report, 33 Daesh members trying to enter Hit with their explosives were neutralized.
Iraqi forces liberated Hit in April after weeks of fighting,
Elsewhere on Sunday, Iraq's Kurdish fighters managed to wrest control over several villages in northeastern Mosul.
Gruesome violence has plagued the northern and western parts of Iraq ever since Daesh launched an offensive in the Arab state two years ago.
The Iraqi military and volunteer fighters are engaged in joint military operations to win back militant-held regions.
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