Wednesday's statement says 854 civilians and 265 members of the Iraqi security forces were killed, and that 1,946 Iraqis were wounded last month.
The worst-hit city was Baghdad, with 352 civilians killed.
The United Nations says the figures are the "absolute minimum" number of casualties and they do not include deaths in the western Anbar province or other militant-held parts of northern Iraq.
The August death toll stood at 1,420. In June, 2,400 were killed as Sunni militants swept across Iraq, the highest figure since at least April 2005.