The group calling itself al-Tawhid and al-Jihad threatened to kill more foreigners in Iraq, in a video message received on Thursday.
It warned the "time for forgiveness has gone".
The tape showed the three hostages alive, clutching their passports, while one of the captors read a statement before carrying out the execution. The recording has not been broadcast.
Iraqi police have reportedly found the bodies of three lorry drivers on the side of a road north of Baghdad.
Two of them have been identified as Turks but it was not immediately clear if they were the same men shown in the video.
The Turks' deaths come just two days after 12 Nepalese workers were killed by another group in Iraq, the Army of Ansar al-Sunna. The killings have been widely condemned, including by senior Iraqi Muslim bodies.
Meanwhile, France is pressing its diplomatic efforts to win the release of two French journalists held hostage in Iraq.
France's Christian Chesnot (L) and
Georges Malbrunot are hostages
A French Muslim delegation visited Baghdad on Thursday to win the release of the journalists, who have been held since 20 August by a group calling itself the Islamic Army of Iraq.
The group is demanding that France repeal a law banning the Muslim Hijab (headscarf) in state schools, which came into force on Thursday.
Several Turks have been captured during the Iraq conflict alongside dozens of other foreigners and have suffered mixed fortunes at the hands of their captors.
A Turkish lorry driver who had been held captive in Iraq since 7 August was freed on Wednesday. His release coincided with the freeing of seven employees of a Kuwaiti trucking.
And two Turkish engineers captured by an Iraqi group were freed on Sunday after the companies they work for said they would withdraw from Iraq to save their lives.
But the bodies of two Turkish captives were found on 27 August found in the key oil refinery town in the Sunni Muslim belt that stretches north and west from the Iraqi capital.