Militants from a group led by al Qaeda ally Abu Musab al-Zarqawi said they had killed five men and warned those who work with the US-backed government they faced the same fate.
Internet video footage showed five men in civilian clothes lined up and shot repeatedly in the back.
A masked militant on the video said: "These apostates are ... allies with (Iraqi Prime Minister Iyad) Allawi's apostate government and support the American enemy. They are attacking Muslim homes in Ramadi under the pretext of preventing terrorists from entering Iraq. Anyone who follows them will face the same fate".
"To the families of civil defence forces, the National Guard and the police we tell you to say your final goodbyes to your sons before you send them to us. Our reward to your sons is slaughter," he added.
It is believed that around two dozen troopers from the Iraqi National Guard may have been abducted by insurgents in the west of the country, according to an account by a Guard officer earlier this week.
There have been numerous other attacks on National Guards and police in the region and there have been instances of entire busloads being targeted.