Iraqi forces flew the national flag above the main government complex in Ramadi earlier in the day, declaring they had recaptured the city, a provincial capital west of Baghdad, which fell to Islamic State in May.
"2016 will be the year of the big and final victory, when Daesh's presence in Iraq will be terminated," Abadi said in a speech broadcast on state television, using an Arabic acronym for Islamic State that the hardline group rejects.
"We are coming to liberate Mosul and it will be the fatal and final blow to Daesh," he added. Mosul, northern Iraq's main city, is by far the largest population center in the self-proclaimed caliphate Islamic State rules in Iraq and Syria.
The army's apparent capture of Ramadi, capital of Anbar province in the Euphrates River valley west of Baghdad, marks a major milestone for US-trained forces who crumbled when Islamic State fighters charged into Iraq in June 2014.
Soldiers were shown on state television on Monday publicly slaughtering a sheep in an act of celebration.
Gunshots and an explosion could be heard as a state TV reporter interviewed other soldiers celebrating the victory with their automatic weapons held in the air.
US President Barack Obama, vacationing in Hawaii with his family, received an update on Monday on the Iraqi forces' progress in Ramadi, the White House said.
"The continued progress of the Iraqi Security Forces in the fight to retake Ramadi is a testament to their courage and determination, and our shared commitment to push ISIL out of its safe-havens," the White House said in a statement, using an acronym for Islamic State.
Congratulating the Iraqi government, US Defense Secretary Ash Carter said: "The expulsion of ISIL by Iraqi security forces ... is a significant step forward in the campaign to defeat this barbaric group."
In a statement, Carter added: "Now it's important for the Iraqi government ... to seize this opportunity to maintain the peace in Ramadi, prevent the return of ISIL and other extremists, and facilitate the return of Ramadi's citizens back to the city."
American officials said the US-led coalition backing Iraqi forces had carried out more than 630 air strikes in the area over the past six months and provided training and equipment.
The US-led coalition, which includes major European and Arab powers, has been waging an air campaign against Islamic State positions in both Iraq and Syria since a third of Iraqi territory fell to the fighters in mid-2014.
The Iraqi army was humiliated in that advance, abandoning city after city and leaving fleets of American armored vehicles and other weapons in the militants' hands. One of the main challenges of the conflict since then has been rebuilding Iraq's army into a force capable of capturing and holding territory.
Baghdad has said for months it would prove its forces' rebuilt capability by rolling back militant advances in Anbar, a mainly Sunni province encompassing the fertile Euphrates River valley from Baghdad's outskirts to the Syrian border.
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