Citing reports from the United Nations Assistance Mission for Iraq's human rights team, at least 757 people were killed in Nineveh, Diyala, and Salahdin provinces between June 5 and 22.
"This figure," UNHCHR said, "should be viewed very much as a minimum [and] includes a number of verified summary executions and extra-judicial killings of civilians, police, and soldiers who were hors combat."
Another 318 people were killed in Baghdad and southern areas during the same time period, many by vehicle-borne improvised explosive devices.
UNAMI also reported 1,189 were injured and an unspecified number abducted.
UNHCHR spokesman Rupert Colville issued a plea on Tuesday for accountability: "We urge the Iraqi authorities to swiftly carry out their obligation to thoroughly investigate these, and any other, reported summary executions and all other violations by their personnel, and to make a concerted effort to bring all perpetrators to justice."