But the urbane, soft-spoken cleric's biggest challenge is likely to be his efforts to win over the pampered and elite Islamic Revolutionary Guards Corps, the hard-line military force created by Ayatollah Ruhollah Khomeini in 1980 to protect the fundamentalist regime and which now wields immense economic as well as political power in Iran.
Witness the storm of protest from IRGC chiefs when Foreign Minister Javad Zarif, who negotiated the ground-breaking interim agreement on Iran's nuclear program with the United States and its allies in November, observed Iran should take the military threat posed by the United States seriously as it has little fear of Tehran's military defenses.
Stressing diplomacy rather than military confrontation will benefit Iran, Zarif declared: "Do you think the U.S., which can destroy all our military systems with one bomb, is scared of our military system?"
Maj. Gen. Mohammad Jafari, the IRGC's overall commander who answers only to Supreme Leader Ayatollah Ali Khamenei accused Zarif of betraying the Islamic Republic and being "infected by Western doctrine."
The exchange underlined how far Rouhani has moved since his stunning landslide victory in presidential polls June 15, when he pledged to move Iran forward into a new era and the extent of the struggle he now faces from the IRGC and other hard-liners bitterly opposed to change.
The 125,000-strong IRGC is the most powerful military force in Iran, and Rouhani, a centrist and longtime insider, has been careful not to provoke the Guards -- or Khamenei, their master -- too far, as did Mahmoud Ahmadinejad, Rouhani's messianic predecessor who fell because he challenged Khamenei's authority.
Even so, in September he openly called on the Guards to stay out of politics, using Khomeini's own stricture they should not be politicized.
"The IRGC is above and beyond political currents, not beside them or within them," Rouhani told Guard commanders Sept. 16. "The IRGC has a higher status, which is that of the whole nation."
Whatever they may think of Rouhani's plans to restore Iran's prostrate economy by negotiating an end to withering international sanctions imposed in 2010 to force Tehran to abandon its contentious nuclear program, Jafari and his commanders oppose any agreement that would weaken the Islamic Republic's military capabilities.
The liberal-leaning strategists around Rouhani say the IRGC has become far too powerful in the last decade or so, a process accelerated during Ahmadinejad's quirky and ruinous two-term rule.
He was a former IRGC officer who fought in the 1980-88 war against Iraq and put many of his former comrades in positions of power.
Reversing that without a confrontation about the corps' vested interests will be difficult.
But Rouhani has cannily praised the IRGC's economic prowess and its gains -- many of them made because the IRGC business arm took on projects in energy and construction because Western firms were scared off by the sanctions -- rather than denouncing the questionable business practices that secured their economic empire, often at the expense of the private sector.
"Today, in conditions in which our economy is a target, the IRGC must go into action and take on three or four large national projects," he declared.
"The IRGC is not a rival to the people and the private sector ... The IRGC today must take on important projects that the private sector is not able to take on."
Iran analyst Mehdi Khalaji of the Washington Institute for Near East Policy says Rouhani has persuaded Khamenei "to adjust the IRGC's economic functions" although the new president "has not challenged its role in shaping Iran's nuclear policy."
So long as Rouhani can keep Khamenei on his side, he can be expected to make some progress toward moving Iran into a position where detente with the United States is possible.
"Unlike previous presidents, Rouhani seems unwilling to dominate the IRGC or directly challenge its influence over various aspects of Iran's political and economic life," Khalaji observed.
"Instead, his approach has been to refashion the IRGC's functions through the supreme leader ... rather than taking independent initiative."