The hitherto unknown group said it "slaughtered three elements from the Iraqi National Guard on charges of spying for, and collaboration with, US forces," the TV said on Wednesday.
The group provided a video showing the three men "confessing" to spying for US forces and "taking part in raids and the capture of Iraqi resistance fighters," the TV said.
It said the video shows the "execution" of the three but that it would refrain from airing the footage "out of respect for viewers' feelings".
It aired only footage of the three men before they were killed, in which they were shown individually and with a hooded armed man.
Meanwhile, three mutilated bodies were found on Tuesday under a suspension bridge in central Baghdad.
It was not immediately known whether the three bodies were that of the guardsmen shown in the video.
The guardsmen in the video
'confessed' to spying for US forces
The river patrol police found the three unidentified corpses beneath a bridge that leads across the Tigris river into the Green Zone, home to the Iraqi interim government and the US and British embassies, an Iraqi Interior Ministry spokesman said on Wednesday.
The bodies did not appear to be foreign, he said.
A police source said the bodies had been decapitated and US troops had sealed off the area.
Earlier, the al-Qaida-linked Army of Ansar al-Sunna posted a video on its website showing the beheading of "a senior Iraqi army officer" in the northern Iraqi city of Mosul.
It accused him of taking part, "along with his soldiers, in several operations against the mujahidin" in the area "at the behest of his American masters."
Many alleged Iraqi collaborators and foreigners have been beheaded after they were abducted by armed groups in Iraq in the past few months.