The men were kidnapped on September 2 from a stadium they were building on the outskirts of the capital along with two others who were released earlier in the southern city of Basra.
The abductees had appeared in a video days after their capture, apparently held by an armed group that used a familiar Shia Muslim slogan and threatened to attack Turkish interests in Iraq if its demands were not met.
The new video released late on Sunday showed the men sitting below the same slogan, clean-shaven and wearing T-shirts.
The video's authenticity could not be verified. Officials in Iraq and Turkey were not immediately available to comment.
On-screen text said the captors had decided to release the Turks after civilians besieged by Sunni insurgents in the Shia villages of Kefraya and al-Foua in northwestern Syria had been given safe passage.
That deal includes the withdrawal of rebel fighters held up in a mostly government-held area near Lebanon. It was reached in talks backed by Iran, which supports the Syrian government, and Turkey, which supports the rebels.
In the video, one of the Turks reads a statement in Arabic, saying the captors had treated them humanely.
"We hope on this holy day of Eidul Azha that Erdogan will not repeat (his actions) and will respect the innocent people of Iraq and Syria," the man said, referring to Turkish President Tayyip Erdogan. Eidul Azha is an Islamic holiday which ended on Sunday.
The video closes with a warning against breaking promises. It makes no new demands and sets no timeline for the Turks' release. It is not clear which group is responsible for the kidnapping.
Baghdad has struggled to rein in Shia armed groups, seen as a critical deterrent against Islamic State militants who control large swathes of the north and west.
The city has also seen a proliferation in recent years of well-armed criminal gangs carrying out contract killings, kidnappings and extortion.
Qais al-Khazali, head of Iranian-backed militia Asaib Ahl al-Haq, has condemned the Turks' abduction but echoed the captors' demands.
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