Rohani appointed Elham Aminzadeh his vice-president for legal affairs, citing her scientific competence, judicial qualifications and legislative experience, as well as her "moral merits."
Aminzadeh will have to be approved by Iranian lawmakers before being appointed, Monday's report said, as will all members of Rohani's proposed cabinet.
Hard-line Iranian lawmakers have challenged the new president's proposed cabinet makeup, accusing him of nominating pro-Western figures and opposition supporters to ministerial posts.
But Rohani told parliament on Monday that his government's priority will be to ease tensions with the outside world and improve the sanctions-battered economy.
The remarks came as a debate over the proposed Cabinet got under way in parliament. It's expected to take three days with lawmakers voting on each of the 18-member Cabinet on Wednesday.
Rohani won a landslide victory in June presidential elections, defeating his conservative rivals. He took the oath of office on Aug. 4 and sent his proposed Cabinet list to the parliament the same day.
Rohani has urged for dialogue with the West over Iran's controversial nuclear program.
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