Rouhani, a cleric and former nuclear negotiator, said he would lead Iran as a moderate. He won presidential elections last week, besting five other challengers seen as conservative supporters of Iranian Supreme Leader Ali Khamenei.
Rouhani told Ezzatolah Zarghami, president of the Islamic Republic of Iran's Broadcasting company, the Iranian media has a vital role to play in his administration.
"An ideal opportunity has been created to promote peace in the country and resolve the [Iranian] people's problems, and media, including the IRIB, are expected to make efforts to maintain and further this opportunity," Rouhani was quoted Friday by state-funded broadcaster Press TV as saying.
Former IRIB Director Ali Akbar Javanfekr pulled out of the presidential contest early this year after consulting with outgoing President Mahmoud Ahmadinejad.
Javanfekr was arrested in 2011 but freed after Ahmadinejad intervened. He was arrested again in September and charged with publishing remarks viewed as contrary to Islamic principles. He was barred from media activities for three years.
Rouhani assumes office in August.