Jan Kubis told the Security Council that supporters of the militant group are also continuing "their vicious terrorist activities against civilians in Iraq and beyond."
With the liberation of Mosul declared on July 10 by Iraq's Prime Minister Haider al-Abadi, the country's coalition-backed forces must now reclaim other IS-controlled territory in parts of Ninawa and Anbar governorates, in Hawija in Kirkuk governorate and in pockets elsewhere, he said.
Since military operations began in October to retake Mosul from IS extremists, he said approximately one million people have been displaced.
Addressing the issue of civilian casualties, Kubis said that at al-Abadi's direction, the liberation operation was marked by "an exceptional effort" by Iraqi forces and their international partners to avoid civilian deaths.
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In stark contact, he said, IS "terrorists showed absolute disregard for human lives and civilisation" by booby-trapping and destroying houses, infrastructure and religious and cultural monuments and deliberately targeting civilians.
Kubis said it is also "crucial" for the government to enforce law and order, the rule of law, justice and accountability as well as implement reforms and good governance practices and promoting development. He said this must also be done in southern Iraq, which was far from the battleground.
"To turn the gains of the military victory into stability, security, justice and development, the government will have to do everything possible to give the people back their lives in society and dignity," the UN special representative said.
He also urged the Iraqi government and the Kurdistan Regional Government, which has announced plans for a referendum Sept. 25 on independence for Kurdistan, to start negotiations "without further delay ... To urgently find common ground" and a roadmap to address critical issues.
These discussions should focus on oil and revenue sharing, the status of disputed territories including Kirkuk, budget issues and relations between the federal government and the Kurdistan Regional Government, Kubis said.