The stoppage this week is reportedly due to staff being repeatedly paid late.
The strikers are also decrying poor working conditions and a failure to adhere to the terms of a settlement that ended the last strike last year.
In November, action had been taken to force management to abandon plans to move the printing of the paper to another company, Pacific Press.
The unions feared job losses as a result of the planned restructure.
Three years ago, the rival daily Les Nouvelles de Tahiti ceased publication after being placed in voluntary liquidation.
La Dépèche de Tahiti was founded in 1964 and was owned by Group Hersant Media between 1988 and 2011. It currently has a circulation of about 15,000.
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