Rouhani is considered a relative moderate amid the hard-line clerics who control Iran. But Supreme Leader Ayatollah Ali Khamenei holds the real power, controlling all important matters of state including the nuclear program.
Just a few weeks ago, President Barack Obama was considering launching a military strike on Syria to retaliate for a chemical weapons attack on Aug. 21 that the U.S. blamed on Bashar Assad's regime. But a U.S.-Russia deal to put Syria's chemical weapons under international control averted military action, at least for now.
Rouhani called his election over the summer a "wise choice of hope, rationality and moderation" and said every issue can be resolved through mutual respect and rejection of violence and extremism.
But elements of his speech were reminiscent of the anti-American rhetoric of his predecessor, Mahmoud Ahmadinejad. He was highly critical of how America projects power and called for a new world order without the U.S. as a superpower.
Clearly referring to the U.S., he said: "Coercive economic and military policies and practices geared to the maintenance and preservation of old superiorities and dominations have been pursued...."
But at the same time, he sent a few signals that there may be room for compromise. He held open the possibility of negotiations on his country's disputed nuclear program as well as talks with the United States to resolve differences.
U.S.-Iranian relations have been frozen for decades, but ahead of Tuesday's events there had been some expectation of a thaw and perhaps even a brief meeting between Rouhani and Obama.
Unlike Ahmadinejad, who denied the Holocaust and called for Israel's destruction, Rouhani never mentioned Israel by name in his speech. But he was highly critical of the "occupation" of Palestine, saying: "Apartheid as a concept can hardly describe the crimes and the institutionalized aggression against the innocent Palestinian people."
Israel's delegation walked out of Rouhani's speech in protest, as it had done in previous years when Ahmadinejad spoke at the U.N.
Prime Minister Benjamin Netanyahu accused Rouhani of "hypocrisy." He said in a statement after the speech that Iran participates in the slaughter of civilians in Syria a reference to its support of Bashar Assad's regime and in carrying out terrorist attacks around the world.
At the U.N., Israeli Minister for Strategic and Intelligence Affairs Yuval Steinitz called Rouhani's rhetoric a "game of deception." He said: "Rouhani came here today in order to cheat the world and unfortunately many people are willing to be cheated."
Steinitz added that Israel has seen no real change on the ground since Rouhani was elected in June.
"Not even one centrifuge was stopped," he said, referring to Iran's uranium enrichment activities.
The United Nations has imposed four rounds of sanctions on Iran for its refusal to halt uranium enrichment a process that can be used to make fuel for both nuclear weapons and nuclear energy. The U.S. and its allies have taken even more devastating measures targeting Iran's ability to conduct international bank transfers and to export oil.
"Unjust sanctions ... are intrinsically inhumane and against peace," Rouhani said. "It is not the states and the political elite that are targeted, but rather, it is the common people who are victimized by these sanctions."
The United States and its Western allies accuse Iran of seeking to develop a nuclear weapon. But Iran insists its nuclear program is purely peaceful a point Rouhani reiterated by saying: "This has been, and will always be, the objective of the Islamic Republic of Iran."
Nuclear negotiations between Iran and six world powers have been stalled for months but Iran agreed to a new meeting this Thursday on the sidelines of the General Assembly.
Rouhani reiterated Iran's right under the Nuclear Nonproliferation Treaty to enrich uranium.
On the conditions that world powers recognize that right and insist that all nations' nuclear programs are for peace purposes only, he said Iran "is prepared to engage immediately in time-bound and result-oriented talks."
"Nuclear weapons and other weapons of mass destruction have no place in Iran's security and defense doctrine, and contradict our fundamental religious and ethical convictions," he claimed. "Our national interests make it imperative that we remove any and all reasonable concerns about Iran's peaceful nuclear program."
Rouhani praised Syria's willingness to accept the international treaty barring the use of chemical weapons. Without naming any nations, he warned that "illegitimate and ineffective threat" to use military force in Syria "will only lead to further exacerbation of violence and crisis in the region."
Rouhani said he listened to Obama's speech to the General Assembly earlier Tuesday and is also open to talks with the United States.
"Commensurate with the political will of the leadership in the United States and hoping that they will refrain from following the short-sighted interest of warmongering pressure groups, we can arrive at a framework to manage differences," he said.
"To this end, equal footing, mutual respect, and the recognized principles of international law should govern the interactions," Rouhani said.
Saying that he has repeatedly heard that "the military option is on the table" a phrase U.S. leaders have used in relation to Iran's nuclear program Rouhani said "let me say loud and clear that 'peace is within reach.'"