Make no mistake; this victory alone does not eliminate ISIS and there is still a tough fight ahead.
But officials warned of other challenges in Iraq.
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, a senior commander in the elite Counter-Terrorism Service, said the jihadist-held territory had been reduced to an area of the Old City of about 200 by 100 metres (yards).
But "operations are in their final stages", and "it is likely that (the fighting) will end today", Aridhi said.
But the report highlights also that the Iraqi government and the US-led coalition forces had "committed repeated violations of worldwide humanitarian law, some of which may amount to war crimes".
Much of Mosul has been destroyed in grinding street-to-street fighting.
Sporadic clashes have continued in the city of Mosul, despite the Iraqi government's declaration of victory against so-called Islamic State there.
UNESCO declares Hebron's Old City a World Heritage Site
In a secret ballot vote 12 countries approved the inscription of Hebron's Old Town and the Cave, three objected and six abstained. A general view of the West Bank city of Hebron with the Cave of the Patriarchs, on January 18, 2017.
"The most fitting response, after the horrors inflicted on countless individuals and communities across northern Iraq by ISIL, the enormous loss of civilian life, and the destruction of livelihoods, homes and infrastructure, is to step up efforts to create an Iraq grounded in equality and the rule of law", the United Nations official said.
Amnesty International, meanwhile, proclaimed the battle for Mosul to be a "civilian catastrophe", with more than 5,800 noncombatants killed in the western part of the city.
Later Monday afternoon, following the initial exchange, the Iraqi Security Forces saw a wave of suicide attacks, and Townsend's assessment of the incident was that it was an attempt to get the Iraqi Security Forces to allow a large group of ISIS fighters close enough to spring a suicide attack.
"For the expected offensives in Hawijah, Tal Afar and western Anbar, where approximately 1,50,000 civilians are thought to still be trapped, it is vital that lessons are learnt from pass offensives", they said, calling for access to safety and assistance to be prioritised.
Still, he was pleased to hear that the leaders of the Iraqi Security Forces were only willing to accept unconditional surrender.
Iran, a key ally of Abadi's Shiite-led government, gave its congratulations too and offered help in rebuilding.
The UN official noted that there have also been allegations of human rights violations and abuses by the Iraqi and associated forces, as well as by individuals taking revenge against captured IS fighters or people accused of supporting them.