The tape from the Army of Ansar al-Sunna appeared on Sunday to show the heads of three young men being severed and placed on top of their bodies.
The three men were shown introducing themselves as Kurdistan Democratic Party (KDP) members and showing their identification papers.
The group said in a statement, also carried on the website http://ansar-alsunnah.8k.com/, that the bodies of the three "agents" were left near Mosul to serve as an "example".
"The puppet Kurdish groups ... have pledged allegiance to the crusaders and continue to fight Islam and its people," said the statement signed by the group and dated Sunday.
The group said it had ambushed the three men near Taji, a town just north of the Iraqi capital Baghdad, as they were moving military vehicles to a base in northern Iraq.
But a local journalist gave a different account.
"Three young Kurds were coming back from Baghdad en route to Zakho in their private car which broke down, so they asked for help at a police station," said Bakhtiar Talabani.
He added that one of the victim's fathers told him the men were kidnapped from the police station.
"There are hidden hands in the police station who handed them to terrorists."