Rouhani also has suggested he could use his time in the U.S. to reach out indirectly to the White House to restart nuclear talks, which have been on hold after a series of dead-end rounds.
"All the signals and talk about trying to reset Iran's relations and policies with the West could be put to the test at the U.N.," said Merhzad Boroujerdi, director of the Middle East Studies program at Syracuse University. "Everything Rouhani does and says will be very closely watched."
He has expressed eagerness to get the nuclear negotiations back on track. This call is apparently echoed by Iran's true decision-makers the ruling clerics and their backers led by the Revolutionary Guard, who often use the president to carry their views.
So Rouhani's appeals to restart the dialogue with the six-nation group the five permanent U.N. Security Council members plus Germany is certain to be cleared at the top.
Rouhani said Tuesday he expects meetings with U.S. envoys and others on a timetable and venue for the talks, last held in April in Kazakhstan amid stalemate.
Iran says no progress can be made until the West rolls back economic sanctions. The U.S. and allies want Iran to make major concessions on its uranium enrichment program, which the West fears could one day churn out weapons-grade material. Iran says it only seeks reactors for energy and isotopes for medical therapy and often cites a religious decree by the country's Supreme Leader Ayatollah Ali Khamenei that describes nuclear weapons as against Islam.
Rouhani has given no clear signs on whether Iran could significantly shift its negotiation positions. In speeches, however, he has not veered from Iran's demands to keep its uranium enrichment labs and its denunciations of sanctions as deal-killing pressures. Instead, he has offered only vague hints of seeking a new way forward.
"On the nuclear issue, the endgame should be a win-win," Rouhani said on Iranian state TV. "A win-lose game is meaningless. We are ready for this game. This job will begin in New York."
He warned, however, that he wants to return to Tehran with some progress to show.
"The world should know that that the time span for settling nuclear issues will not be unlimited," Rouhani said. "The world should use the opportunity that the Iranian nation has provided through the election."
Part of his unexpected victory in June is a cadre of Western-educated Cabinet members and advisers. Among them is Zarif, who is scheduled to accompany him to New York. Zarif served at Iran's U.N. Mission from 2002 to 2007.
Rouhani also received permission from the ruling clerics to make a potentially important shift in the negotiation team: taking control of the talks from security agencies and giving it to Zarif and his diplomats. His presence in New York adds significant weight to efforts at reviving the nuclear dialogue.
Zarif said he expects no direct talks with U.S. officials but could meet with former members of the Obama administration or other former policy-shapers.
Washington officials have not spoken publicly about Zarif's claim of a letter exchange with Rouhani on the Syrian civil war.
Some Iranian news agencies have reported that a message from Obama was carried to Iran last month by Oman's ruler, Sultan Qaboos bin Said, whose country was a mediator before when Iran released three Americans convicted of espionage despite claims they innocently crossed the border while hiking in Iraq in 2009.
The Obama administration has indicated interest in possible groundbreaking one-on-one nuclear talks with Iran after nearly 35 years of diplomatic estrangement. Envoys from Iran and the U.S. have previously held meetings on Iraq mediated by Baghdad officials.
The push for possible Iran-U.S. dialogue received a boost by the alleged chemical weapons attack in Syria, which the U.S. and allies have blamed on Assad's forces.
Obama has suggested Iran a strong opponent of chemical weapons could help pressure ally Assad into accepting a Russian-brokered plan to surrender stockpiles of lethal gas to international control. Iran suffered chemical attacks from Saddam Hussein's forces then backed by Washington in the 1980-88 war with Iraq.
"The use of chemical weapons is a crime, we believe it is a crime against humanity, but we believe that also the use of force, the threat of use of force, is also a criminal offense in international law," Zarif told state-run Press TV Wednesday. "Unfortunately, it seems to me that the United States seems to be living in the 19th century when the use of force was a prerogative of states. It is not."
On Thursday, Rouhani made his first trip abroad since his inauguration in August, to the Kyrgyzstan summit of the Shanghai Cooperation Organization, a regional bloc. Rouhani is expected to hold separate talks with the leaders of Russia and China both key to any international consensus over Assad's chemical arsenal.
Tehran-based political analyst Saeed Leilaz believes Rouhani "will restore balance in Iran's foreign policy through reviving relations with the West and clarifying its ties with the East."
The conservative Iranian news website alif.ir urged Rouhani to use his time in New York for intense diplomacy rather than spotlight-grabbing like Ahmadinejad.
"We hope that the president, far from the annual hue and cry of the previous administration, defends Iran's stance strongly," it said. "Rouhani should ... use the opportunity to seek to end sanctions as well as regional disputes and conflict."
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Murphy reported from Dubai, United Arab Emirates.
