An order issued by the US-led Coalition Provisional Authority in 2004 before the Iraqi government gained sovereignty gives American security companies immunity from Iraqi prosecution on issues arising from their contracts.
The UN said the order "enables the US government to waive a contractor's immunity" but "to UNAMI'S knowledge it has not done so to date".
The UN report, which covers the period from April 1 to June 30, cited instances in which at least 88 civilians were said to have been killed in air strikes, including seven children who died when helicopters allegedly attacked an elementary school near the Iranian border in the volatile Diyala province.
The US military has said it is investigating the report.
But the UN agency said the findings of such investigations "are not systematically publicised".
It also detailed the alleged killing of 15 Iraqi civilians during US raid and search operations, including a 14-year-old boy.