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His victory in the June 14 vote has lifted hopes of a thaw in Iran's antagonistic relations with the West that might create openings for defusing its nuclear dispute with world powers. Rohani has pledged a more conciliatory approach than Mahmoud Ahmadinejad, under whose belligerent presidency the Islamic Republic drew ever more punishing international sanctions.
Rohani's pledge of an inclusive cabinet could reassure conservative hardliners who look askance at the endorsement he was granted by reformists in the election.
In turn, reformists will hope to regain some political influence - with the aim of easing repression at home and Iran's isolation abroad - after being sidelined under Ahmadinejad, who by law could not run for a third consecutive term.
"The future government must operate in the framework of moderation ... [and it] must avoid extremism, and this message is for everyone," Rohani, a former chief nuclear negotiator, said in a speech carried live on state television.
"The next cabinet will be trans-factional ... This government is not obligated to any party or faction, and will work to choose the most qualified people from all sides and factions, under conditions of moderation and temperance."
Analysts say Rohani, a mid-ranking Shi'ite Muslim cleric who has held sensitive security posts since the 1980s, enjoys an insider status and close relationship with theocratic Supreme Leader Ayatollah Ali Khamenei, and may be able to build bridges between factions to yield reforms.
But Khamenei will retain the final say on policies that most concern world powers, including Iran's nuclear program and its support for Syrian President Bashar Assad against rebels trying to overthrow him.
Rohani also urged moderation in Iranian policies toward the rest of the world and called for a balance between "realism" and pursuing the ideals of the Islamic Republic.
"Moderation in foreign policy is neither submission nor antagonism, neither passivity nor confrontation. Moderation is effective and constructive interaction with the world," he said.
"The Islamic Republic of Iran, as a major regional power or the biggest regional power ... must play its role and for this we need moderation."
Western powers suspect Iran of seeking to develop a nuclear weapons capability, which Tehran denies. The Islamic Republic is now languishing under increasingly tough sanctions limiting its oil sales, a crucial source of revenue, obstructing its foreign trade and stoking higher inflation and unemployment.
Iran's friends and foes indicated shortly after Rohani's election triumph they did not believe it would bring fundamental change in Iranian foreign policy.
Tehran is at loggerheads with Western powers on a range of foreign policy issues including its shadowy nuclear program and its support for Syria's Assad, the Lebanese Shi'ite militant movement Hezbollah and the Palestinian Islamist group Hamas.
U.S.-allied Gulf Arab countries have also accused Iran of interfering in their affairs, though Tehran denies trying to subvert Saudi Arabia and its wealthy Gulf neighbors.
Rohani, who will take office in early August, said he was dedicated to "mutual relaxation of tensions" with other states.