(CNN) -- Next week's United Nations meeting could mark a turning point in the acidic relationship between Iran and the United States: Will President Barack Obama shake the hand of newly elected Iranian President Hassan Rouhani? Will the two presidents even hold a meeting?
Analysts were divided about Rouhani and his sincerity in addressing his country's nuclear program, which Iran insists is for peaceful energy but which the United States and others suspect is for atomic bombs.
In many ways, Rouhani's recent election is like Obama's in 2008: Rouhani enjoys enormous political capital, offering an opportunity to renew U.S.-Iran relations.
Rouhani overcame hard-line conservatives by campaigning as a centrist and a reformer, using a "hope and prudence" slogan.
To keep hard-liners at bay, Rouhani now must deliver something -- namely, economic relief as Iran strains under global sanctions -- or his critics will prevail as they did against Obama in 2009 when his own venture on U.S.-Iran diplomacy foundered, one analyst said.
"Now the roles are reversed: Rouhani needs to strike a deal quickly," said Trita Parsi, president of the National Iranian American Council who's authored "A Single Roll of the Dice: Obama's Diplomacy with Iran."
Next week's U.N. General Assembly meeting "could be quite decisive," Parsi said.
"That's going to be the moment where the two sides have to invest the political capital needed. Otherwise it will go nowhere. It's going to be costly politically to strike a deal. There's going to be critics on both sides," Parsi said. "There is a need for a huge dose of political will to be injected into the process."
But Elliott Abrams, a senior fellow at the Council on Foreign Relations, said Obama shouldn't meet with Rouhani during the U.N. gathering, though shaking hands in a corridor would be appropriate.
"They are not counterparts, they are not equal," said Abrams, who also supervised U.S. policy in the Middle East under former President George W. Bush.
While Rouhani is Iran's president, he is not the country's leader. Ayatollah Ali Khamenei is the supreme leader of Iran.
"So for the president to meet with him, I think confers too great a recognition on him," Abrams said of an Obama-Rouhani meeting.
Abrams described Rouhani as a skilled political tactician when he was the country's chief nuclear negotiator from 2003 to 2005.
"Remember this is the guy -- Rouhani -- who wrote several years ago with pride how he tied us up in negotiations while the nuclear program (of Iran) was going forward," Abrams said. "So we should approach this with skepticism."
The Obama administration has welcomed Rouhani's published column.
"But the fact of the matter is actions are what are going to be determinative here," White House spokesman Josh Earnest said. "The Iranians, for a number of years now, have been unwilling to live up to their obligations to the international community as it relates to their nuclear program."
The international community's economic sanctions against Iran has "taken a significant toll on their economy and put pressure on them to come back to the bargaining table," Earnest said.
Earnest did acknowledge how Rouhani now enjoys a window of opportunity against his hard-line adversaries at home, but Iran must "demonstrate their seriousness of purpose" and show "their nuclear program is for exclusively peaceful means."
For now, Obama's schedule next week doesn't contain any meetings with Iranian representatives, Earnest said.
When asked if the United States is willing to ease sanctions against Iran, Earnest said such economic pressure "is what has brought the Iranians to the table."
Where analysts agree is how Rouhani has launched a media campaign through his op-ed, which was covered extensively.
Rouhani wants "a constructive approach" between his country and the world, including about Iran's nuclear program, he wrote. The dispute about why Iran is seeking nuclear capability -- for energy or for bombs -- has prompted international sanctions and escalated concerns about additional warfare in the Middle East.
"We must work together to end the unhealthy rivalries and interferences that fuel violence and drive us apart," Rouhani said.
Rouhani's Twitter account even retweeted how CNN gave him coverage.
Rouhani doesn't write his own tweets; that's done by personnel in his office, an Iranian official told CNN.
The Iranian government, however, blocks Twitter and other social media in Iran, rendering the president's tweets as messages to the outside world only, though many Iranians circumvent the blockage.
Parsi couldn't recall an Iranian president ever writing for the Washington Post, largely because "there would be backlash at home," he said.
Abrams concurred about Rouhani's publicity blitz.
"There's a major charm offensive underway," he said. "The question is whether there is any substance to it."