Rouhani's message last week also carried a subtext for Saudi Arabia and the other Western-allied Persian Gulf states. As Iran's diplomatic profile rises with attempts to recalibrate its dealings with Washington, the Gulf rulers will have to make adjustments, too.
That's not such an easy thing for the monarchs and sheiks to swallow.
Leaders such as Saudi King Abdullah are accustomed to having Washington's undivided focus and a prominent voice in shaping policies over Iran, which Gulf officials routinely denounce for allegedly trying to undermine their rule through suspected proxies and spies.
The prospect of Iran and the U.S. becoming something less than arch foes — a flirtation at the U.N. General Assembly capped by President Barack Obama's groundbreaking telephone call to Rouhani — pushes the Gulf states toward unfamiliar territory.
They certainly remain a pillar of U.S. diplomatic and military strategy in the region, with key bases and one of the State Department's main Iran listening posts in Dubai. But a core reason for the cozy ties — beyond maintaining reliable oil supplies — has been mutual worries over Iran. That basis could now be chipped away slightly as Tehran and Washington explore possible direct talks over Iran's nuclear program.
If nothing else, the Gulf's Arab leaders may have to compete a bit harder for the White House's ear.
"So much of the Gulf relationship with Washington has been built on the concerns over Iran: the U.S. bases, the huge Gulf arms purchases, the protection of oil shipments," said Theodore Karasik, a security and political affairs analyst at the Dubai-based Institute for Near East and Gulf Military Analysis.
"All of a sudden, here's the chance that the U.S. and Iran could start talking directly. That cuts the Gulf out of a loop somewhat," he added.
Washington's Gulf partners have already been feeling slightly under-appreciated.
When then-Secretary of State Hillary Rodham Clinton visited the region last year she heard a list of complaints that included worries about Obama's perceived strategic emphasis on Asia and how Washington failed to stand by their common ally, Egypt's Hosni Mubarak, during the Arab Spring uprisings.
And the Gulf leaders — strong backers of Syria's rebel forces — could hardly contain their displeasure when the U.S. pulled back from possible military action against Bashar Assad's regime in favor of a Russian plan seeking the dismantlement of Damascus' chemical arsenal.
A former U.S. diplomat in the region said that a senior Saudi official grumbled to him recently: I wish the Americans stood by us like the Russians stand by Assad. The diplomat spoke on condition of anonymity because the conversation recounted was private.
"There will no doubt be some tensions between the Obama administration and Gulf leaders" over Syria, said Ayham Kamel, a Middle East analyst at the Eurasia Group in London.
Iran, though, is an issue even closer to home.
The diplomatic energy lavished on Rouhani by Washington — particularly at last week's U.N. General Assembly — is likely to leave Gulf leader questioning their place in the U.S. pecking order if there is a thaw in the 34-year diplomatic freeze between the U.S. and Iran.
Such a prospect may still seem distant. Iranian hard-liners have made it clear they are highly uneasy with the fast-paced overtures at the U.N.
Iran's Deputy Foreign Minister Abbas Araghchi tried to address the worries even as his boss, Foreign Minister Mohammad Javad Zarif, stayed behind in the U.S. to continue his pitch for a quick resolution to the nuclear impasse — that would, Iran insists, include easing sanctions.
"Definitely, a history of high tensions between Tehran and Washington will not go back to normal relations due to a phone call, meeting or negotiation," Araghchi was quoted as saying Sunday by the semiofficial Fars news agency.
He added: "We never trust America 100 percent. And, in the future, we will remain on the same path. We will never trust them 100 percent."
In the Gulf, Sunni Arab leaders view Shiite power Iran with deep suspicion. In some ways, Gulf views on Iran are often more in line with Israel than other Arab states.
A leaked U.S. diplomatic cable described how Saudi's King Abdullah urged in 2008 for a U.S.-led attack against Iran to "cut off the head of the snake" and cripple its nuclear weapons program, which Saudi officials and others fear could touch off a frightening nuclear arms race in the region.
More recently, arrests of alleged Iranian espionage rings have been announced in Saudi Arabia and Kuwait. In Bahrain — where the Western-backed government accused Iran of encouraging a Shiite-led uprising since 2011 — a court Sunday sentenced 50 people to prison sentences ranging from five to 15 years on charges that include spying for Iran.
"Arab countries in the region are watching the talks between Iran and the U.S. with concern in their hearts," said Mahdi Motaharnia, a professor of international politics in Qom Azad University in Iran. "They fear that many concessions they were receiving from the West because of tensions between Iran and the U.S. could be in jeopardy."
Clearly, the overall U.S. ties with the Gulf are too extensive and strategic to suffer any major blows. The Pentagon's footholds include air bases, thousands of ground troops in Kuwait and the U.S. Navy's 5th Fleet in Bahrain. Gulf nations spend billions on the latest U.S. weapons.
It's more about the Gulf perceptions that Washington's policies are no longer closely overlaid with their own, said Sami al-Faraj, director of the Kuwait Center for Strategic Studies and a security adviser to the six-nation Gulf Cooperation Council.
"The Gulf states once believed they always had American in their corner," said al-Faraj. "Syria changed that. What's happening in Iran may change it even more."
Associated Press writers Nasser Karimi in Terhan, Iran, and Barbara Surk in Beirut contributed to this report.
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