In a statement signed by the Secret Action Group of al-Mahdi Army and posted on the internet on Friday, the captors said the journalist would be released on Saturday since he opposed the policies of the US administration.
"As for the American journalist we have, we will release him tomorrow, Saturday, in the afternoon, because he disagrees very much with the American administration," the statement said.
The captive was not named in the statement, but all indications are that it referred to the US journalist Micah Garen.
Threat to oil
An archaeological reporter and manager of New York-based Four Corners Media, Garen was seized last week in the southern Iraqi city of Nasiriya.
As well as covering thefts of archaeological artefacts in Iraq the documentary organisation's website says it is working on "documenting the life and experiences of American soldiers on the front lines in Iraq".
The captors' internet statement also threatened to destroy oil facilities in southern Iraq if US troops and Iraqi government forces did not leave Najaf.
"If you do not withdraw from Najaf by 11pm on Saturday, Baghdad time, we will set alight and explode at least 75% of pipelines and wells in south Iraq," it said.
Iraqi fighters have in recent months waged a campaign of kidnapping aimed at driving out individuals, companies and troops supporting US-led occupation forces and the new Iraqi interim administration.