The Association of Iranian Journalists was closed down shortly after the swearing in of former hardline president Mahmoud Ahmadinejad in 2009.
The closure was ordered by Tehran's former prosecutor Saeed Mortazavi following a complaint lodged by the intelligence ministry.
"In a letter, some 772 Iranian journalists urged the president to unseal their association," Etemad reported.
"You promised to do your best to reopen the journalists association ... While in the past few months some efforts were made by your ministers in this regard, the exact time of reopening is not clear for us yet," the petition reads.
The Association of Iranian Journalists is an affiliate of the International Federation of Journalists, which strongly condemned the closure.
Rouhani, a reputed moderate who defeated conservatives in last year's election, promised more social freedoms during his election campaign.
