Iraq's Prime Minister Haider al-Abadi declared the "total victory" in Mosul on Monday evening - after a almost nine-month-long battle with IS fighters.
That battle could start "in the coming weeks", Townsend said.
The report also notes that the coalition must publicly acknowledge the human cost of the fighting in Mosul.
A senior U.S. commander in Iraq has warned that the war against so-called Islamic State (IS) is not over, despite a "historic" victory in Mosul.
Aside from Isis's atrocities, however, many in Mosul have also died as a result of US-led coalition bombing.
Mosul resident Hind Mahmoud said by telephone that she had heard exchanges of gunfire in the Old City and seen an Iraqi army helicopter firing on IS militants on Tuesday. The biggest challenge to the Iraqi government and its partners will be rebuilding the city back from the ground up.
And few citizens remain in the area.
October 21 IS militants and sleeper cells carry out a coordinated wave of attacks, shootings and suicide blasts in the central city of Kirkuk, killing at least 80 people in an attempt to divert attention from the attack on Mosul.
Iraqi forces were earlier today still fighting to eliminate the last pockets of IS resistance in Mosul, with jihadist fighters surrounded in a sliver of territory in Mosul's Old City.
The UN High Commissioner for Human Rights called for alleged violations by all sides to be fully investigated and those responsible to be held accountable. As the battle space constricted, the coalition began approving airstrikes dropping bombs of 200 pounds or more on IS targets within 50 meters (yards) of friendly forces.
The last days of the fight for Mosul were the fiercest, he said.
"The armed group then prevented civilians from evacuation, in some cases trapping them inside their homes by welding their doors shut or rigging the entrances with booby traps".
However, the Iraqi defence ministry was not immediately available to comment on the Amnesty report.
Col Scrocca described the allegations as "irresponsible and an insult" to the troops who had died freeing civilians in Mosul from IS rule.
"I think it is in the final decision-making stages", Townsend said, although he expected the footprint to be smaller.
Zeid described Mosul's fall as the "turning point" in the conflict against ISIS, but warned that the group continues to subject people to "daily horrors" in its remaining strongholds of Tal Afar, west of Mosul, and in Hawijah, north of Baghdad.
February 19 Iraqi forces begun the assault on western Mosul. According to United Nations estimates, building the bare-minimum and most important infrastructure of the city will cost nearly $1 billion.
"They do not accept to surrender", Aridhi told AFP.
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