"Then they handcuffed them with plastic tape and shot them in the head with guns fitted with silencers."
Mohammad al-Askari, of the defence ministry, said 24 people had been arrested from another Sunni village nearby with links to al-Qaeda.
"According to our investigation the perpetrators came from a village around 500m away.
"They are from the same tribe. They were around 25 armed men, wearing military uniform.
"One of them could say a few words in English to give the impression that this was a joint Iraqi-American patrol.
"They had with them a list of names, they knocked at the door, called out a name, then took the man or the woman who came out to a grove and killed them."
He added: "Our investigation has shown that they came from a village loyal to al-Qaeda network."
The village of Sufiya where the attack happened lies in a mainly Sunni area that used to be an insurgent stronghold.
In the past two years there have been many attacks aimed at punishing or intimidating Sunnis, but this is one of the bloodiest for some time, says the BBC's Jim Muir in Baghdad.
It shows that al-Qaeda or its allies are still in business, though much less effective than in the past, he adds, and there is no evidence they are regaining hearts and minds within the Sunni community.
The Sunni militias that lent their support to the government are known as Awakening Councils, or the Sons of Iraq.
US authorities set up the militias, paying, arming and training their members before Iraqi authorities took control of them in late 2008.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.