The Turkish men, who were working on a football stadium project, were seized in Baghdad's Sadr City area earlier this month, and militants presenting themselves as a Shiite group claimed the kidnappings in a video posted online.
"We demand the release of the kidnapped men and the end of such practices, which harm the image of Islam" in general and Shiites specifically, Sistani's office said in a statement.
Such actions also lead to "reducing the prestige of the state and weakening the elected government," the statement on Sistani's website said.
The words "We are at your service, O Hussein" - a reference to the Prophet Mohammed's grandson, who is one of the most revered figures in Shiite Islam - appeared behind the gunmen.
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And one of their demands was that Turkey order rebel forces to stop besieging four Shiite villages in northern Syria.
This all indicates the militants are Shiite, but could also potentially be an attempt to mislead, and the group's make-up and provenance were not immediately clear.
Iraq's autonomous Kurdish region is independently exporting oil via Turkey in a move the federal government considers illegal - a point of contention between Baghdad and Ankara.
"If Erdogan and his party do not respond, we will crush Turkish interests and their agents in Iraq by the most violent means," the group said in the video, which lacked the polished production quality found in most militant propaganda in Iraq.
But Sadr City is a stronghold of Shiite paramilitary forces opposed to the jihadists.
A soldier was killed last week when security forces clashed with the Shiite Ketaeb Hezbollah militia while searching for a person allegedly involved in the kidnappings.
The security command responsible for the capital said there had been intelligence that "one of the members of the gang that carried out the kidnapping" was on Baghdad's Palestine Street.