Lawmaker Intisar al-Jabouri from Nineveh province, where Mosul is the capital, said uprooting IS' "extremism ideology" was the key to peace in Mosul, which reeled under the group's harsh rule for three years.
"I announce from here the end and the failure and the collapse of the terrorist state of falsehood and terrorism which the terrorist Daesh announced from Mosul", Haider al-Abadi said in a speech shown on state television, using an Arabic acronym for ISIL.
The senior United States commander in Iraq, Lt Col Stephen Townsend, said Iraq's Shia Arab-led government had to reach out to the Sunni Arab minority community to ensure IS did not return after being defeated militarily in the rest of the country.
Dozens of members of the security forces erupted into cheers after he spoke, dancing and waving flags and their weapons as they celebrated.
"This victory alone does not eliminate (IS) and there is still a tough fight ahead".
Lt. Gen. Stephen Townsend tells Pentagon reporters that he doesn't see a significant expansion of the US and coalition effort in Raqqa.
"Now it is time for all Iraqis to unite to ensure (IS) is defeated across the rest of Iraq", Townsend said.
Meanwhile, airstrikes and exchanges of gunfire could still be heard in the narrow streets of Mosul's Old City on Monday, where IS has staged its last stand.
Abadi said that as well as continuing to tackle IS, Iraq had other challenges including "the mission of stabilization and the mission of building".
Iraqi forces are pushing to retake the last patch of ground in Mosul where Islamic State militants are holding on to a tiny sliver of the Old City, west of the Tigris River, a day after the prime minister visited soldiers to congratulate his troops on the hard-fought battle.
At least one air strike hit the Old City, the scene of fierce battles with IS, sending a plume of smoke into the air early on Tuesday.
Lieutenant General Sami al-Aridhi of Iraq's elite Counter-Terrorism Service said the jihadists had been reduced to an area of the Old City of about 200 by 100 metres (yards).
The report, which covered the first five months of 2017, noted how the militants moved civilians with them around Mosul, prevented them from escaping and created battle spaces with dense civilian populations, while Iraqi forces and the coalition "failed to adapt their tactics".