In recent weeks, fighters from the Islamic State of Iraq and the Levant have spearheaded a lightning offensive across Iraq, plunging it into its deepest crisis since the last US troops left in 2011.
The al-Qaeda breakaway group now controls territory stretching from northern Syria as far as the outskirts of Baghdad in central Iraq.
The figures exclude deaths in embattled Anbar province, which is largely controlled by Sunni militants.
The second deadliest month this year was May, with 799 Iraqis killed, including 603 civilians. April's death toll was 750.
Also Read
The latest casualty figures exceed even last year's peak. The UN reported that last July at least 1,057 Iraqis were killed and another 2,326 were wounded.
"The staggering number of civilian casualties in one month points to the urgent need for all to ensure that civilians are protected," the UN Special Representative in Iraq, Nickolay Mladenov, said in the statement.
Iraq's new parliament holds its inaugural session today. The country's top Shiite cleric urged lawmakers last week to agree on a prime minister before meeting in hopes of averting months of wrangling that could further destabilize the country.
The Islamic State meanwhile announced the establishment of its own government, or caliphate, ruled by Islamic law. It proclaimed its leader, Abu Bakr al-Baghdadi, a highly ambitious Iraqi militant with a USD 10 million US bounty on his head, to be the caliph, and it demanded that Muslims around the world pledge allegiance to him.