On Saturday, the group said it was giving the government 48 hours to free all Sunni women held in Iraq's prisons or it would kill the 20 men, who were abducted northeast of Baghdad.
The group also demanded that the government hand over to it what it called interior ministry agents accused of involvement in the widely publicised alleged rape of a Sunni woman and other reported killings of Sunnis and rapes.
The video showed close-ups of the abducted men's identification tags, including that of a ministry security unit commander.
The authenticity of the tape could not be verified, but it was posted on websites often used by al-Qaeda.
The group, which was formed last year by al-Qaeda's wing in Iraq and several smaller groups, has claimed responsibility for mass kidnappings and a series of major attacks.