The video shows an apparent training session with masked boys wearing ammunition belts, forcing a man off his bicycle at gunpoint and marching him off down a muddy lane.
At one point in the video, the boys swear allegiance to al-Qaeda.
The US military said the videos were found during a raid in December at Khan Bani Saad, northeast of Baghdad.
Smith said the films were made in Iraq and depicted Iraqi children, but offered no definitive evidence to back up the claim.
"We believe this video is used as propaganda to send out to recruit other boys ... and to send a broader message across Iraq to indoctrinate youth into al-Qaeda," Smith said.
It is rare for children to be behind armed attacks in Iraq but they have been used as decoys.
Smith said the military decided to show the videos of children to expose al-Qaeda's "morally broken ideology" and encourage Iraqi opposition to it.
Mohammed al-Askari, Iraq's defence ministry spokesman, said he believed opposition fighters were abducting an increasing number of Iraqi children, although he could not give details or figures.
"This is not only to recruit them, but also to demand ransom to fund the operations of al-Qaeda," al-Askari said.
He showed a video clip which he said featured Iraqi security forces rescuing an 11-year-old boy who had been kidnapped by al-Qaeda in Iraq.