Confronting suspicions about his readiness to deal, Rouhani told a news conference before leaving New York on Friday that his government would present a plan in three weeks on how to resolve the impasse.
"I expect this trip will be the first step and the beginning of constructive relations with countries of the world," said Rouhani, who attended the U.N. General Assembly's ministerial session last week.
Until then, a senior Obama administration official said, Obama's foreign policy team will watch for signs that Rouhani truly is engaged in a "different calculation" trying to decide whether defying the U.S. and others on the nuclear issue is worth the pain of sanctions that have damaged Iran's economy.
The official spoke on condition of anonymity to discuss internal White House thinking.
The United States, through the United Nations and unilaterally in some cases, has been the driving force behind the penalties that have isolated Iran from the world economy.
"Now the big question is can the Iranians hold it together to make the very painful political concessions that will be necessary to win sanctions relief," said R. Nicholas Burns, a Harvard professor and career U.S. diplomat in both Democratic and Republican administrations who formerly served as lead negotiator on Iran's nuclear program.
Rouhani insists that Iran's supreme leader, Ayatollah Ali Khamenei, the gatekeeper for every decision on matters of state, has given his government the power to negotiate an end to more than three decades of U.S.-Iranian estrangement.
But that cannot happen, Washington and its close allies say, as long as Tehran refuses to open its nuclear program to international inspections and proves its claim that it is enriching uranium only to fuel domestic energy and medical research programs. Uranium enriched to low levels can be used to produce energy; at higher levels, it can be used for a weapon.
Sanctions are linked to Iran's refusal to halt uranium enrichment, and Rouhani said in his U.N. speech last week that Iran has the right under the Nuclear Nonproliferation Treaty to continue to enrich uranium. It was one of the reminders of how difficult it will be to bridge the gaps with the West in nuclear negotiations.
In Obama's address to the General Assembly, he said no nation wanted to deny Iran a nuclear energy program. What remains at issue are deep suspicions that Iran is enriching uranium to levels far beyond what is needed to fuel electricity-generating reactors or to produce medical isotopes.
Israel is particularly skeptical of Iran's intentions, citing past declarations by Iranian officials that the Jewish state should be wiped from the map.
Israel is constantly on guard against the Shiite militant group Hezbollah, which virtually rules southern Lebanon along Israel's northern border. The powerful Iranian Revolutionary Guard has armed Hezbollah with increasingly sophisticated rockets that could strike deep into Israel.
The Revolutionary Guard, which has tentacles deep in the Iranian economy and has been the enforcer of its hostile policies toward the West and Israel, could try to undermine Rouhani's opening to the West.
So the rapidly shifting political ground raises questions about how the Guard might react to a policy that could challenge its regional footholds not only with Hezbollah in Lebanon but also its deep support of Syrian leader Bashar Assad in that country's civil war.
Israeli Prime Minister Benjamin Netanyahu will need assurances of American skepticism when he visits the U.S. this week. Netanyahu said Sunday he is going to the United Nations to "tell the truth in the face of the sweet-talk and the onslaught of smiles," a reference to Iran's diplomatic overtures to the West.
As is always the case in the Middle East, one event hopes for a solution to Iran's nuclear program, for example is tangled in the threads of politics elsewhere in the region. That's particularly so now.
Having threatened Assad with a unilateral military strike over the use of chemical weapons, Obama backtracked and sought congressional approval first. But then the Russians stepped in as guarantors of a plan to have Assad turn his weapons over the international inspectors for destruction.
Russia also had blocked U.S. requests for U.N. resolution against Syria, before reversing course and, with the rest of the U.N. Security Council, supporting a measure that includes the threat of penalties should Assad renege on the agreement.
That resolution, adopted Friday, gives breathing room and certainly will draw in the Iranians, given their deep involvement with Assad, while the U.S. and Russia work toward a political solution in Syria.
Obama insists the military option against Syria remains on the table, but domestic hawks aren't satisfied.
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EDITOR'S NOTE Steven R. Hurst is The Associated Press' international political writer, based in Washington, and has covered foreign policy for 35 years, including extended assignments in Russia and the Middle East.
