It says 1,241 civilians were killed in June - a nearly 40% drop compared with 1,951 violent deaths in May.
However, the figures cannot be verified independently, and many deaths are believed to go unreported.
June also ended the deadliest three months for US soldiers since the war began in 2003, with 330 troops killed.
US officials say American losses are rising because increased patrols in and around the Iraqi capital have left their forces more exposed.
Five US soldiers were killed in separate attacks in Baghdad and the western Anbar province on Sunday, the US military said.
US President George W Bush has ordered nearly 30,000 troops to be deployed in and around Baghdad to try to improve security and curb sectarian violence.
The last of the US reinforcements arrived last month.
The new Iraqi government figure means that continuous bombings and shootings claimed an average of 40 lives every day in June - a drop from about 60 civilian deaths a day in May.
It also shows that at least 170 Iraqi policemen and soldiers were killed in the past month.
Anywhere else in the world it would be appalling statistics, but for Iraq this figure is seen as a positive sign, the BBC's Andrew North in Baghdad says.
US commanders said they were cautiously optimistic about the new figure but added that it was too early to say it was a sign their troop surge was working.
There are suspicions about the way the Iraqi government handles such information, our correspondent says.
It has refused to reconsider its decision to withhold statistics from the
United Nations mission in Iraq.
Iraq civilian deaths 'dropping' source
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